Legislative Branch Appropriations Act, 2006 - Title I: Legislative Branch Appropriations - Makes FY2006 appropriations for the Senate for: (1) expense allowances; (2) representation allowances for the Majority and Minority Leaders; (3) salaries of specified officers, employees, and committees (including the Committee on Appropriations); (4) agency contributions for employee benefits; (5) inquiries and investigations; (6) the U.S. Senate Caucus on International Narcotics Control; (7) the Offices of the Secretary and of the Sergeant at Arms and Doorkeeper (Sergeant at Arms) of the Senate; (8) miscellaneous items; (9) the Senators' Official Personnel and Office Expense Account; and (10) official mail costs. (Sec. 2) Amends the Supplemental Appropriations Act, 1977 to increase from eight to nine the number of individual consultants the Majority and Minority Leaders may each appoint. (Sec. 3) Amends Public Law 101-302 to extend through FY2006 and each fiscal year thereafter the authorization of funds within the Senate contingent fund for expenses of the U.S. Senate Collection. (Sec. 4) Amends Public Law 108-83 to permit the use of Senate contingent funds for expenditures, up to $10,000 in any fiscal year, for meals and refreshments in Capitol facilities in connection with official activities of the Senate Commission on Art or other authorized programs or activities. (Sec. 5) Amends the Revised Statutes to repeal the requirement that the Secretary of the Senate, under certain conditions, deduct from a Senator's monthly or periodic payments the amount of his or her salary for each day such Senator is absent from the Senate. (Sec. 6) Amends the Legislative Branch Appropriations Act, 1999 to provide that the authority of the Senate Committee on Appropriations to procure the services of individual consultants or organizations does not need the approval of, nor does it have to report to, the Committee on Rules and Administration. Makes appropriations for the House of Representatives for FY2006 for: (1) salaries and/or expenses of the House leadership offices, committees (including the Committee on Appropriations), officers and employees, and the Child Care Center; and (2) Members' representational allowances. (Sec. 101) Requires that any amounts appropriated for a representational allowance for a Member of the House for FY2006 which remain after all payments are made under it be deposited in the Treasury and used for deficit reduction or, if there is no federal budget deficit after all such payments have been made, to reduce the federal debt. Makes FY2006 appropriations for salaries and/or expenses of: (1) the Joint Economic and Taxation Committees; (2) the Office of the Attending Physician; (3) the Capitol Guide Service and Special Services Office; (4) the preparation of statements of appropriations for both the House and the Senate; and (5) the Capitol Police. (Sec. 1002) Prohibits the Capitol Police from operating a mounted horse unit during FY2006 or any succeeding fiscal year. Requires the Chief of the Capitol Police to transfer to the Chief of the U.S. Park Police the horses, equipment, and supplies of the Capitol Police mounted horse unit. (Sec. 1003) Amends the Ethics in Government Act of 1978 to require an officer or employee of the Capitol Police, beginning in calendar 2005, to file annual financial disclosure reports with the Clerk of the House. (Sec. 1004) Establishes in the U.S. Capitol Police the Office of the Inspector General. Prohibits the reduction, except in certain circumstances, of the pay or benefits of any employee of offices or entities whose duties and responsibilities are transferred to the Office of Inspector General. Requires financial statements prepared by the Chief Administrative Officer (CAO) of the Capitol Police to be audited by the Inspector General or by an independent public accountant, as determined by the Inspector General. (Currently, the CAO provides for such audit by an independent public accountant.) (Sec. 1005) Requires the Chief of the Capitol Police to submit to Congress a detailed, itemized semiannual report of disbursements for U.S. Capitol Police operations. Prescribes the semiannual periods as October 1 through March 31 and April 1 through September 30. (Sec. 1006) Amends the Legislative Branch Appropriations Act, 2004 to establish FY2006 limits on the number of Capitol Police officers to be hired for Library of Congress duty. Makes the Memorandum of Understanding between the Library of Congress and the Capitol Police entered into on December 12, 2004, effective through FY2006, subject to such modifications that may be made in accordance with the modification and dispute resolution provisions of such Memorandum. (Sec. 1007) Prohibits individuals to whom overtime compensation was paid under the Legislative Branch Appropriations Act, 2003 in violation of the restrictions applicable to the payment of such compensation under such Act from being required to repay the compensation if the compensation was paid for services provided before June 15, 2005. Excepts from this prohibition against required repayment any officers or employees of the U.S. Capitol Police whose annual salary is specified in statute and is not established under the schedule of rates of basic pay established and maintained by the Capitol Police Board. Makes FY2006 appropriations for salaries and/or expenses of: (1) the Office of Compliance; (2) the Congressional Budget Office (CBO); (3) the Architect of the Capitol (AOC), including for the care and operation of Capitol buildings and grounds, Senate and House office buildings, the Capitol power plant, Library of Congress buildings and grounds, Capitol Police buildings and grounds, the Botanic Garden (including for the care and operation of the National Garden but not for its construction); (4) the Capitol Visitor Center; and (5) the Library of Congress for salaries and expenses (including rescission of funds), the Copyright Office, Congressional Research Service (CRS), and Books for the Blind and Physically Handicapped. Earmarks funds for Books for the Blind and Physically Handicapped to reimburse the National Federation of the Blind for costs incurred in the operation of its NEWSLINE program. (Sec. 1100) Permits the Congressional Budget Office (CBO), in certain circumstances, to waive claims against its employees for overpayment of pay allowances, and of travel, transportation, and relocation expenses and allowances. (Sec. 1201) Amends the Legislative Branch Appropriations Act, 1991 to increase from eight to nine the number of positions under the AOC's jurisdiction whose rate of basic pay may be fixed by the AOC up to 135% of the minimum rate for GS-15. (Sec. 1202) Amends the 2002 Supplemental Appropriations Act for Further Recovery From and Response To Terrorist Attacks on the United States relating to the AOC's authority to acquire facilities for computer backup for offices in the legislative branch. Allows the AOC, in the case of a building or facility acquired through purchase for such purposes, to enter into or assume a lease with another person for the use of any portion of the building or facility that is not required for such purposes, subject to the approval of the entity which approved the acquisition. (Sec. 1301) Authorizes the expenditure of up to $5,000 for the incentive awards program of the Library of Congress. (Sec. 1302) Establishes an upper limit $109.943 million for the FY2006 obligational authority of the Library of Congress with regard to certain reimbursable and revolving fund activities. Authorizes the Librarian of Congress, subject to specified conditions, to transfer temporarily up to $1.9 million of funds appropriated in this Act for Library of Congress salaries and expenses to the revolving fund for the FEDLINK Program and the Federal Research Program established under the Library of Congress Fiscal Operations Improvement Act of 2000. (Sec. 1303) Amends the Miscellaneous Appropriations Act, 2001 to provide that up to a specified amount out of additional funds made available for the National Digital Information Infrastructure and Preservation Program shall remain available until expended, and may be used for competitive grants to state governmental entities, without regard to any matching contribution requirement, to work cooperatively to collect and preserve at-risk digital state and local government information. (Sec. 1304) Makes funds available for the Library of Congress under this Act available for transfer to the Department of State as remittance for a fee charged by the Department for FY2006 for the maintenance, upgrade, or construction of U.S. diplomatic facilities, but only to the extent that the amount of the fee so charged is equal to or less than the unreimbursed value of the services provided during FY2006 to the Library of Congress on State Department diplomatic facilities. (Sec. 1305) Amends the Legislative Branch Appropriations Act, 1996 to repeal the prohibition against obligational authority under the heading "Library of Congress" for activities in support of parliamentary development, except for Russia, Ukraine, Albania, Slovakia, and Romania. (Sec. 1306) Library of Congress Digital Collections and Educational Curricula Act of 2005 - Requires the Librarian of Congress to administer a program to teach educators and librarians how to incorporate the digital collections of the Library of Congress into educational curricula. Authorizes the Librarian to: (1) establish an educational consortium to support the program; and (2) make funds appropriated for the program available to consortium members, educational institutions, and libraries. Authorizes appropriations. (Sec. 1307) Library of Congress Inspector General Act of 2005 - Establishes in the Library of Congress an Office of Inspector General to: (1) conduct and supervise audits and investigations (excluding incidents involving violence and personal property) relating to the Library of Congress; (2) provide leadership and coordination and recommend policies to promote economy, efficiency, and effectiveness; and (3) provide a means of keeping the Librarian of Congress and Congress fully and currently informed about problems and deficiencies relating to Library administration and operations. Appropriates funds for: (1) the Government Printing Office (GPO) for congressional printing and binding (including transfer of funds); (2) GPO for the Office of Superintendent of Documents for salaries and expenses (including transfer of funds); (3) a payment to the Government Printing Office Revolving Fund; (4) the Government Accountability Office (GAO) for salaries and expenses; (5) a payment to the Open World Leadership Center Trust Fund; and (6) a payment to the John C. Stennis Center for Public Service Development Trust Fund. Title II: General Provisions - (Sec. 201) Sets forth authorized or prohibited uses of funds appropriated by this Act identical or similar to corresponding provisions of the Legislative Branch Appropriations Act, 2005. Title III: Continuity in Representation - (Sec. 301) Amends federal election law concerning the election of Senators and Representatives to require states to hold special elections for the House within 49 days after a vacancy is announced by the Speaker in the extraordinary circumstance that vacancies in representation from the states exceed 100. Waives the 49-day requirement if, during the 75-day period beginning on the date of the vacancy announcement, a regularly scheduled general election or another special election for the office involved is to be held. Requires determination of the candidates who will run in the special election: (1) within 10 days after the vacancy announcement by the political parties authorized by state law to nominate candidates; or (2) by any other method the state considers appropriate. Sets forth requirements for judicial review of any action brought for declaratory or injunctive relief to challenge such a vacancy announcement. Requires a final decision within three days of the filing of such an action. Makes a final decision non-reviewable. Requires a state, in conducting such special election, to ensure to the greatest extent practicable (including through the use of electronic means) that absentee ballots are transmitted to absent uniformed services voters and overseas voters within 15 days after the Speaker announces that the vacancy exists. Requires a state to accept and process any otherwise valid ballot or other election material from an absent uniformed services voter or an overseas voter, as long as the ballot or other material is received by the appropriate state election official within 45 days after the state transmits it to the voter. Applies this subsection to the District of Columbia, the Commonwealth of Puerto Rico, American Samoa, Guam, and the U.S. Virgin Islands.