While the city of Washington used to exist as a legal entity within the District of Columbia, these days it's all just the District. Including both D.C. and Washington, D.C. on the map would be including two names for the same thing.
Map showing the "District" of Columbia: http://maps.google.com/?ie=UTF8&ll=40.010787,-78.09082&#...
Map showing the "City" of Washington: http://maps.google.com/?ie=UTF8&ll=38.548165,-77.34375&#...
Why not just list them both?