You will file a Part-Year Resident State Return for both Maryland and DC.
You'll need to adjust your W-2 income to properly reflect the wages you received while living in each state.
In the state interviews, you'll be presented with a Federal amount for wages, then asked for the MD or DC amount. The amount may be filled in according to your W-2, but you can change the amount to correctly report income earned in that state.
Here's more info on How to File a Part-Year Resident Return.