Your income from working in NC is fully taxable by NC, and you must file a non-resident NC tax return. Your home state of TN does not tax earnings from work.
Boxes 15-17 of your W-2 will show any NC taxes that were withheld by your employer.
If the boxes are blank, and assuming your W-2 is correct, it would mean that no NC taxes were withheld for you.
But your NC income remains taxable by NC regardless.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
