It depends
If she is covered under MSRRA , she will only file taxes in your state of legal residency (SLR). So if NC is not your SLR, then she will need to file a NC nonresident state income tax return to claim a full refund of her withholdings.
In order to get the full refund of her NC state income tax withholdings, she will need to file a nonresident NC return but report zero "0" income from NC (even though she does have NC wage income). She must mail in this NC nonresident state income tax return and include her state W-2 information. She will want to include an explanatory statement with her NC return stating her situation (that her NC employer withheld NC state income taxes from her wages in error because she is a military spouse and covered under MSRRA).
You can add a state under the state taxes tab in TurboTax.
However, if she does not qualifies under the MSRRA and you and your wife are residents of different states, then you can still file jointly for federal income tax but will need to file married filing separately for state taxes.
https://ttlc.intuit.com/replies/3301995
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