You will need to file a Maryland Resident tax return and a Delaware Nonresident tax return. Delaware will tax you on the money you earned working there, and Maryland will give you a credit for tax paid to Delaware, so that you don't pay state tax twice on the same dollar of income.
Prepare the Delaware Nonresident tax return first, and then when you prepare the Maryland Resident return TurboTax will automatically "pick up" the tax paid to Delaware for the credit calculation.
Otherwise, just follow the TurboTax state tax return "interview" questions carefully.
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