Wage earners pay tax to their resident state.  Sounds like that's MD in this case.  Good luck getting money out of DC.  What tax year are we talking about?

Normally you would file a D-40B to get the withholding back but I'm not sure what the process would be if "Client filed taxes for only DC" already.  You might call DC and see what they say, they may need you to amend the D-40 that was already filed.

@sjrcpa may have a better idea.

Rick