No, if you moved and the W2 was not updated, you do not need to pay the state tax on that reporting error. Be aware that the state of New Jersey will most likely contact you by mail regarding the tax on this income. You will need to provide proof that you moved before Jan. 1, 2017. You may need to send copies of closing papers on a new home or rent receipts and an updated driver's license to prove that you have moved.
