About all you can do right now is to talk to the payroll/HR people where you work, to make sure they are going to report your NC income on your W-2 based upon your move date. IF you transferred to their TN location and started working in TN before you actually moved to TN, they may have been continuing to withhold NC taxes, since NC taxes would be needed if you worked in TN wile living across the border in NC (that happens a lot for cross border workers where the TN job is close by).
Then you would have had to notify HR/Payroll of your new address immediately after the move, so they could stop withholding for NC......but yeah, even if you did that, such things can fall thru the crack. But talk to payroll now with your move date records in-hand, and see if they will report NC W-2 wages properly based on date you moved. Keep all your paystubs for all of 2019 too, or print them all out if they are online, in case you do end up having to mess around with the numbers at tax time. There is a way to re-adjust the NC wage during the NC-PY interview, but it is better if the employer gets them reported properly in the first place to avoid NC coming back at you asking questions later if you end up having to "adjust" them when you file.
You will have to file an NC Part-Year tax return at tax time, and it is unlikely that you will get all your NC withholding back. NC-PY tax returns calculate PY taxes by calculating a tax based on ALL your yearly income, and then ratioing the tax down based on what % of your total year's income you received while living in NC. So, unless your total year's income is really low, there will be some NC taxes retained by NC.
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*
