If you were a part year NJ resident and then you moved to NYC, you would file a Part Year Return for both NY and NJ.
Where did you work while living in each state? If you worked in NY while living in NJ, you would take a credit on your NJ taxes for taxes paid to NY while living in NJ or vice versa if you lived in NY and worked in NJ. You would only take a credit for the time you lived in the state that you did not work in.