When should my NJ State Taxes come in if my federal came in a month prior

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There's no connection between your federal refund and your New Jersey refund. The New Jersey Division of Taxation says that processing an e-filed tax return takes a minimum of 4 weeks and a mailed tax return takes a minimum of 12 weeks. You can check the status of your New Jersey refund at the following link.

https://www.state.nj.us/treasury/taxation/checkrefundstatus.shtml