@aa2014 --
Then you are a part-year resident of NJ. If you continued to have NJ-source income after your relocation, then (as you suspected) you must file both a part-year resident and a non-resident NJ return. See page 5 of this NJ tax publication:
https://www.nj.gov/treasury/taxation/pdf/pubs/tgi-ee/git6.pdf
The publication also provides detailed filing instructions for your situation.
In the Personal Info section of TT, enter your State of Residence as "Foreign or U.S. Possession". It's the last choice in the State of Residence drop-down list. Your State of Residence for tax purposes is your State of Residence as of year's end.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
