Not quite correct, your employer is liable to withhold tax for DC, not VA.
DC and VA do have a reciprocal agreement. If you live in DC, VA does not withhold state tax for VA. You only pay income tax to DC.
If your 2021 W-2 has VA state tax withholdings, you need to file a VA nonresident return and claim the refund.
You need to fill out this exemption form VA-4 and submit it to your employer.
@amc12341
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