If you live in Virginia (VA), but your employer withheld taxes for DC, then you can file the DC return to receive a refund because VA & DC have a reciprocal agreement. Reciprocal agreements cover wages only.
File the VA return as a full year resident, taxing all worldwide income, then file the DC return as a nonresident with zero income.
If you received other types of income such as sale of property, it is reported on the state return where the property was situated. And your resident state return where you can receive a "credit for taxes paid to another state" so that you don't actually pay tax on it twice.
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