If your gambling winnings were $10,000 or less then you are not required to file a nonresident New Jersey return. Otherwise, you are required to report your winnings. Please view the section labeled Exempt (Nonreportable) Income on page 18 in the New Jersey link below.
http://www.state.nj.us/treasury/taxation/pdf/current/1040nri.pdf
If you are required to file a nonresident state return then follow the directions below to do so.
https://ttlc.intuit.com/replies/3302052
