@abDC -- The PA tax office is correct. If you live in any other state and work in DC, you don't have to file a DC tax return. But that only works in reverse for DC residents who work in Maryland or Virginia.
Therefore DC residents with PA-source income must file a non-resident PA return in addition to their DC return. Those taxpayers will be able to take a credit on their DC return for the taxes paid to PA, so they won't be double-taxed.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
