Yes, for tax year 2023 you have to file a part-year resident tax return in both DC and MD.
Since DC and MD have tax reciprocity, ALL the income you earned while a resident of DC is taxable by DC, and ALL the income you earned while a resident of MD is taxable by MD. Reciprocity means that you are only taxed by your resident state.
In the Personal Info section of TT, enter your state of residence as DC, and indicate that you also lived in MD. You became a resident of DC on the day you began living in DC with the intent of making it your new main, primary home. Answer NO to the question about having income from another state.
You should enter your W-2's as is, but you should allocate your income to either DC or MD according to your dates of residence in each. Whether you owe taxes or get a refund will depend on whether or not your withheld taxes exceed your taxes due.
As @SteamTrain said, you cannot apply one state's refund to pay another state's tax bill.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
