No. Maryland and Virginia have reciprocity. Employee-based income is only taxed by the resident state.
Also, unemployment by a nonresident of Maryland is not deemed to be Maryland source income, even if the unemployment is paid by Maryland.
http://forms.marylandtaxes.com/16_forms/nonresident_booklet.pdf (Page 7)
Refunds of state or local income taxes, pensions, annuities, IRA distributions, unemployment compensation and Social Security or Railroad Retirement benefits are not considered to be from Maryland sources for income tax purposes when these items are received by a nonresident of Maryland.
