No- you don't need to file a Virginia tax return. VA and MD are reciprocal states. If you live in one and work in the other, you only file taxes in your resident state.
Did you have VA taxes withheld? If VA taxes were withheld, you would have to file with VA just to get that back. You would then have to ensure that the VA withholding stopped ASAP.
https://ttlc.intuit.com/questions/2895760-which-states-have-reciprocal-agreements
