Since you only lived part of the year in New Jersey, you will want to file a part-year resident form for NJ and then you can allocate the income to that return that was earned when you lived in the state. Be sure to set up in TurboTax that you lived in more than one state during the year in the Personal Info tab section. Below is more information on filing a part-year resident return in TurboTax, except that note where the instructions say the MY INFO tab is meant for online TurboTax users, as for CD/Download versions you select the Personal Info tab:
https://ttlc.intuit.com/replies/3302008
