Maryland has reciprocal agreements with District of Columbia, as well as Pennsylvania, Virginia, and West Virginia. If your employer withheld tax for one of the reciprocal states, you can claim a refund from the reciprocal state. You cannot claim a credit on your resident return for the reciprocal state. If DC tax was not withheld from your pay check, you do not need to file a DC return. If it was withheld, you will need to file a DC return to get a refund. You do have to claim the income on your Maryland tax return.
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