N.J. Stat. § 40:56-61
On the making of assessments for benefits, the officer or board, or majority of such board, shall also at the same time fix and determine the amount, if any, that any property is damaged incidentally to the making of the improvement, but exclusive of damages for real estate taken. The amount of such incidental damages accruing to any parcel of real estate shall be deducted from the amount of any benefits assessed thereon.
If the amount of such damages as confirmed by the Superior Court shall exceed the benefits assessed upon any parcel of real estate, or if no benefits shall accrue thereto, the excess or the amount of such damages may be raised or appropriated as provided by law, and shall be paid by such city of the first class to the owner of any such parcel of real estate so damaged. If it is uncertain as to who is to receive any award of such damages, the amount thereof may, with leave of the Superior Court, be paid into said court and shall there be distributed according to law to the person or persons entitled thereto.
N.J.S. § 40:56-61