Technically no...
Although Washington has at times achieved a measure of home rule, the federal government remains the ultimate authority in the District. The so-called federal interest in the nation’s capital is protected by Congress’s right to veto any legislation passed by the city council; Congress also reviews the District’s budget. Congress provides an amount of money, the federal payment, to the District to compensate for the absence of a property tax on federally owned property in the city. Congress also retains the right to make laws pertaining to the District, such as building height restrictions.
The Home Rule Act (1973) provided for an elected 13-member city council and an elected mayor for the District of Columbia. Because of corruption, mismanagement, and a shrinking tax base, the District experienced a severe fiscal crisis in the late 1980s and early ‘90s. Congress in 1995 established a financial control board with broad powers to overhaul municipal services. In 1996, declaring that the city’s public schools were in deplorable condition, the financial control board appointed a board of trustees to take over the responsibilities of the elected board of education.
Since 1971 the District has elected a nonvoting delegate to the House of Representatives. Residents have been permitted to vote in presidential elections since 1964.
Just like all Americans, residents of Washington, DC:
# pay federal and local taxes;
# serve in the armed forces and make sacrifices in times of war and conflict;
# serve on juries to uphold federal laws and policies.
Yet, DC residents are denied voting representation in the US Senate and the US House of Representatives, and do not have complete autonomy over their own budget and local laws. The Congress - representing everyone except DC residents - has the final say on DC's budget and laws.
DC elects a Delegate to the House of Representatives who can vote in committee and draft legislation, but does not have full voting rights. The current Delegate is Congresswoman Eleanor Holmes Norton.
Additionally, DC residents elect two shadow senators and a shadow representative as non-voting representatives who lobby Congress on District issues and concerns. Currently, the District is represented by Shadow Senator Paul Strauss, Shadow Senator Florence Pendleton, and Shadow Representative Ray Browne.