NO.
If you are a NJ resident and have PA state income taxes withheld, you need to talk to your payroll office and have the withholding stopped. The should have a form for you to complete and sign. This applies to STATE withholding, you are still subject to PA local income tax withholding.
If you had PA taxes withheld in 2015, you will need to file a PA nonresident return showing zero income and get a full refund of the taxes withheld.
Then file a NJ resident return reporting all income, including that earned in PA. You may use any local tax withholding as a tax paid in another state to obtain a credit on your NJ resident return.
For more info, see:
http://www.state.nj.us/treasury/taxation/njit25.shtml
