More from VA's tax site, if your employer withheld for you in both DC and VA:

Nonresidents:

If you are a resident of a reciprocity state, accept employment in Virginia, and meet the criteria for exemption, complete Form VA-4 to certify your exemption and give the form to your employer. You will need to re-certify your exemption every year.

If your employer withholds Virginia income tax and you find out that you are exempt, correct your withholding information with your employer for the future, and file Form 763-S to claim a refund.