District of Columbia Government Improvement and Efficiency Act of 1996

District of Columbia Government Improvement and Efficiency Act of 1996 - Reduces the minimum number of members of the Board of Trustees of the American University from 40 to 25. (Sec. 3) Repeals the application of the Service Contract Act of 1965 with respect to the District of Columbia. (Sec. 4) Authorizes the Mayor of the District and the Director of the Bureau of Prisons, with respect to District of Columbia convicts in any Federal penitentiary during the five-year period beginning in FY 1997, to enter into an agreement waiving requirements relating to the cost of the care and custody of D.C. convicts in Federal penitentiaries or establishing an alternative amount to be charged against the District for such convicts so long as the Director provides at least 15 days' notice of the intent to enter into the agreement to specified congressional committees. (Sec. 5) Amends the District of Columbia Self-Government and Governmental Reorganization Act to exempt from review by the D.C. Council contracts: (1) entered into by the Washington Convention Center Authority for preconstruction activities, project management, design, or construction; (2) entered into by the District of Columbia Water and Sewer Authority, other than contracts for the sale or lease of the Blue Plains Wastewater Treatment Plant; and (3) for Federal highway improvement projects at the option of the Council. (Sec. 6) Amends the District of Columbia Government Comprehensive Merit Personnel Act of 1978 to allow, at the request of the Inspector General, the Director of Personnel to waive the residency requirement for employees of the Office of the Inspector General. (Sec. 7) Requires members of the Judicial Nomination Commission to serve without compensation for services rendered in connection with their official duties on the Commission. (Sec. 8) Renames the District of Columbia Self-Government and Governmental Reorganization Act as the District of Columbia Home Rule Act.