If your wife claims TX residency, then she would not be subject to NC tax on her NC income. She may, however, have to file a NC return.
If her employer did not withhold NC tax, then she would not need to file a NC return.
If her employer withheld NC tax, she would have to file an NC return to get that tax refunded. She can stop future NC withholding by filing a Form NC-4EZ to claim exemption from state withholding under MSRRA (see below).
Make sure you answer the federal and state tax interview questions carefully. Active-duty military are considered to live in their state HOR no matter where they are stationed. Their active-duty pay is considered to be earned in their state HOR. When you complete the My Info Personal Interview (both you and your wife):
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Select Texas as your state of residence;
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Answer "No" when asked if you "Lived in another state in 2020?" That question only applies if you changed your state of residence in 2020.
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When asked if you "Earned money in another state?", answer "No" (unless the military member had non-military income in the state where you are stationed).
Under the "Military Spouse Residency Relief Act" (MSRRA), your wife is afforded some protection from state income taxes when living outside her state of residence because of your military assignment. Twenty-two states (including NC), however, require that active duty military member and his/her spouse be residents of the same state in order for the spouse to enjoy the income tax protections of the MSRRA.
For additional information, see Military Spouses and State Taxes
