Yes you should file a Part-Year Resident return for NJ because of the sale of the residence. The state of New Jersey does not tax Unemployment Insurance benefits, they are subject to federal income taxes.
Also, NJ has what is termed an exit tax. Rather, it is a withholding tax that New Jersey requires at the closing of a real estate transfer when a New Jersey resident is leaving the state, The withholding would be the greater of 2% of the sales price of the home or 8.97% of the gain on the sale.”
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