For 2019, you are part year residents of both states. You lived in Georgia for two or three months and you continue to work there.
State tax is withheld based on where the work is done, so even if you change your address to your North Carolina address, they will still withhold Georgia taxes as long as you are working in Georgia.
You will have to file a Georgia part year resident tax return. If you have income in North Carolina, you may have to file a North Carolina part year resident return as well.
For 2020, you will have to file a non-resident Georgia tax return and a resident tax return in North Carolina. You will able to take a credit for the taxes paid to Georgia on your North Carolina tax return.
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