It is not in any state.
After the US Constitution (1787) provided that a tract of land be reserved for the seat of the federal government, both Maryland and Virginia offered parcels for that purpose; on 16 July 1790, Congress authorized George Washington to choose a site not more than 10 mi (16 km) square along the Potomac River. President Washington made his selection in January 1791 and then appointed Andrew Ellicott to survey the area and employed Pierre Charles L'Enfant, a French military engineer who had served in the Continental Army, to draw up plans for the federal city.
On 3 May 1802, the city of Washington was incorporated (the District also included other local entities), with an elected council and a mayor appointed by the president.
http://www.city-data.com/states/District-of-Columbia-History.html
Fairfax County ceded the land of current day Arlington County to the Federal Government in 1789 as part of the District of Columbia, was returned to Virginia in 1846. First called Alexandria, in 1920 it took the name of the Custis-Lee estate.
Arlington County is an urban county of about 203,000 residents in the Commonwealth of Virginia, in the U.S., directly across the Potomac River from Washington, D.C. Originally part of the District of Columbia, the land now comprising the county was retroceded to Virginia in a July 9, 1846 act of Congress that took effect in 1847. At a land area of 26 square miles, it is geographically the smallest self-governing county in the United States.
It is the location of Arlington National Cemetery, Washington National Airport, and the Pentagon.
https://en.wikipedia.org/wiki/Arlington,_Virginia
