A non-resident of DC cannot file a DC tax return. DC income tax applies only to DC residents. DC does not even have non-resident tax return forms.
You can work in VA even if your employer cannot withhold VA income tax for you. You would simply have to make quarterly estimated tax payments to VA. See this reference for the details on that:
https://www.tax.virginia.gov/individual-estimated-tax-payments
If you choose to work in DC while keeping your residence in VA, then you will be subject only to VA income tax.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
