Washington, D.C. Admission Act This bill provides for admission into the United States of the state of Washington, Douglass Commonwealth, composed of most of the territory of the District of Columbia. The commonwealth shall be admitted to the Union on an equal footing with the other states. The Mayor of the District of Columbia shall issue a proclamation for the first elections to Congress of two Senators and one Representative of the commonwealth. The bill applies current District laws to the commonwealth and continues pending judicial proceedings. The commonwealth (1) shall consist of all District territory, with specified exclusions for federal buildings and monuments, including the principal federal monuments, the White House, the Capitol Building, the U.S. Supreme Court Building, and the federal executive, legislative, and judicial office buildings located adjacent to the Mall and the Capitol Building; and (2) may not impose taxes on federal property except as Congress permits. District territory excluded from the commonwealth shall be known as the Capital and shall be the seat of the federal government. The bill maintains the federal government's authority over military lands and specified other property. The bill provides for expedited consideration of a joint resolution repealing the Twenty-third Amendment to the Constitution, which provides for the appointment of electors of the President and Vice President. The bill continues certain federal authorities and responsibilities, including regarding employee benefits, agencies, courts, and college tuition assistance, until the commonwealth certifies that it is prepared to take over the authorities and responsibilities. The bill establishes the Statehood Transition Commission to advise the President, Congress, and District and commonwealth leaders on the transition.