Tennessee does not impose an income tax. They only tax interest and dividend income as part of their Hall income tax.
Please see the attached link for more information.
States without income tax for individuals
As for your state income taxes, if you never changed your state of residence from North Carolina, you should have been filing state income tax returns there. However, if you changed your state of residency to Tennessee, then you would not have had to file any income taxes in North Carolina.
North Carolina filing requirements for Active Military
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