You generally owe taxes to the state where you live and to the state(s) where you worked.
So although you did not "live" in DC (because it was not your domicile), you did work there.
So you owe DC 1) a non-resident tax return, and 2) you owe DC taxes for the time you worked in DC, even before and after you moved to Northern Virginia, so long as you were working in DC.
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