Yes, you will file both returns based on the facts you present. If you were not a resident of DC, you will have to file a DC nonresident request for a refund to get these mistaken withholdings returned to you. DC only taxes residents of DC (and DC is not a state). However, all of this income will be taxed to your home state of Maryland, which will also require you to file a Maryland resident return. And, unless you also had MD taxes withheld by your employer, you will "rob Peter to pay Paul": get back the DC refund to pay Maryland taxes. You also want to advise your employer to begin withholding the proper Maryland taxes and stop withholding DC taxes.
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