No not is your permanent residence is DC.
If you live in DC, work in VA and your only source of VA income is wages, then you will not need to file a VA state income tax return. (If you selects that you earned income in another state under the personal information tab and VA wages are your only out-of-state income, please go back under the personal information tab and select that you did not make money in another state.)
DC and VA have what is called a state reciprocal agreement. This allows nonresidents to not have state withholding taxes taken out for wages earned in the state. So there should be no DC withholdings being reported on your W-2.
You will need to claim the full amount of your VA wages on your DC resident state tax return.