When mailing a tax return, if you did not use some type of tracking service when the return was mailed you will not know if the tax return was received by the state. The IRS and States do not send any type of acknowledgment that they receive a tax return.
If your tax return had a state tax refund then you should be able to get the status of the state tax refund using the links shown in this TurboTax support FAQ for New Jersey along with links for contacting the NJ Department of Taxation - https://ttlc.intuit.com/questions/2896788-how-do-i-track-my-new-jersey-tax-refund
