If your employer stopped withholding NY tax then you would not have to file a withholding certificate.
The fact that your employer stopped withholding NY tax certainly speaks in your favor if your choose to get all your withholding back.
People will often go along with NY even if they know they should not pay NY just to avoid an audit. If you lived in a state with an income tax, your home state would give you a credit so there's not much difference in what you pay (though NY is almost always higher, so you are overpaying).
However, TN has no income tax so you will be paying a lot of unnecessary tax if you do not claim your withholding.
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