New Jersey does not have a special form for part-year filers, as part-year resident you must use the regular resident return, Form NJ-1040. The return provides a line for you to show the period of your residency in the state.
If you continued to receive income from New Jersey sources after you moved out of the state, or if you received income from New Jersey sources prior to moving to the state, then you also will have to file a New Jersey nonresident tax return, Form NJ-1040NR.