I'm sorry, I didn't notice that there was no withholding for NJ. I guess when I read that you "took the credit on the Maine return" I thought the tax paid to NJ came from your W-2 withholding.
I'd say don't file a NJ return, but then you'd have to be prepared to respond to the state if they contact you looking for one, because it says NJ wages on your W-2. I say that you should file a return, and indicate that none of the income was earned in NJ, and you wouldn't owe any tax.
But get your employer to stop putting NJ Wages on your W-2.
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