State tax filing
You will need to file two part-year resident returns.
Since you resided in Maryland until November 2020, you need to file your Maryland state return as a part-year resident for that period of time. Your employer should have been withholding taxes in Maryland only at this time. In 2020, D.C. was operating under state reciprocity for any nonresidents only working in D.C. but residing in another state. This means that your income was only taxed in your resident state while you lived in Maryland but worked in D.C.
Once you move to D.C., your employer should have been withholding taxes only in D.C. and not in Maryland anymore.
Since you had taxes withheld in D.C. while you were a resident of Maryland, you will need to report your taxes paid to another state on Form 502CR as you mentioned above. This will ensure you get credit for any taxes paid and reported in D.C. while you were still a resident of Maryland and ensures you are not taxed twice on the same income. You will still be taxed on the income earned while a nonresident of D.C. but any income taxed in both jurisdictions will then be offset by the credit on your Maryland return.
Also, yes you would report your taxes on Form 502 but the section for Part-year resident will be completed on your 2020 income tax return.
