How you file is your choice. If you never set foot in NY, you should not have NY tax withheld.
If you lived in a state with an income tax, there's not too much of a tax difference because your home state will give you credit for NY tax. However, since you live in TN, you're paying a lot of tax you don't need to.
If you do file a nonresident return, consider not spending the refund for at least a year in case NY comes back at you.
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