If your capital gain is totally excluded from the federal return, it is not subject to tax in NJ either.
If NJ income tax was withheld at closing, you will need to file a NJ non resident return (form NJ-1040-NR) to claim a refund. It is possible to get an advance of the refund by filing special form A-3128 after the closing.
Q. If I need to file 2 state returns (current state and New Jersey), how do I do this in Turbo Tax?
A. In the personal info section, you will be asked if you made money in another state. Answer yes, even though you technically didn't. That will get TT to generate the additional state return. You will have to pay a TT fee for the additional state software.
Reference: https://www.state.nj.us/treasury/taxation/documents/pdf/guides/Buying-or-Selling-a-Home-in-New-Jerse...
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