Yes, you will need to file tax returns for both states, plus you will need to notify your employer (if you still work there) to make sure that taxes are taken out for DC instead of Maryland. It is true that Maryland and DC have reciprocity with each other, but you would have needed to notify your employer to not withhold for Maryland by filing an MW 507 form. And, you are correct that you will need to file with these states to get a refund of taxes paid to Maryland, as well as to pay taxes to DC.
Based on your comments above, the assumption is that you lived in DC while working in Maryland and never lived in Maryland during the year. Therefore, if you never lived in Maryland, you will want to file a non-resident return for Maryland. And then if you still live in DC, you would file a resident return for DC. If you do not live in DC now, you would need to file a part-year resident return for DC and include the income that you earned while working in Maryland on it. Then, you would need to file a part-year resident return for the other state you lived in during the year (if that state has income taxes.)
In TurboTax, you will want to be sure the MY INFO section is set up properly. The My Info section can be accessed by selecting it from the black column on the left-hand side of the screen. There you will want to note the state of residence where you currently live, PLUS identify that you LIVED in another state (DC). Then, scroll down the screen and note that you also "made money" in another state (MD). This should trigger TurboTax to help you create the non-resident return for MD, the part-year resident return for DC, as well as the part-year resident return for your current state (again this is an assumption since you stated you lived in DC for six months.)
Here is more information and scenarios related to filing non-resident returns, part-year resident state tax returns, plus living and working in different states. Note that it is recommended that you complete the tax return for the non-resident state first.
Look at the different scenarios in this link:
https://ttlc.intuit.com/replies/3302342
Part-year Resident Returns:
https://ttlc.intuit.com/replies/3302008
Non-Resident Return:
https://ttlc.intuit.com/replies/3302052
