N.J. Stat. § 54:4-8.13
An application for a veteran's deduction hereunder may be filed with the assessor of the taxing district at any time on or before December 31 of the pretax year. If so filed and approved by the assessor, he shall allow a veteran's deduction from taxes on the real or personal property, or both, assessed to the claimant in the amount of the claim approved by him and shall indicate, upon the assessment list and duplicates, the approval thereof in such manner as shall be prescribed by rules of the Director of the Division of Taxation, together with the proportionate share of such property deemed to be owned by the claimant for the purposes of this act, if the claimant is not the sole owner thereof. The application, if not filed with the assessor within the time aforementioned, may be filed with the collector during the tax year and upon approval by the collector of such application he shall determine the amount of the reduction in tax to which the claimant is entitled and shall allow said amount as an offset against the tax then remaining unpaid. If the amount allowable as an offset shall exceed the amount of the tax then unpaid for that tax year, or if the application for a veteran's deduction is not filed with the collector until after all taxes for the tax year have been fully paid, the claimant may make application to the governing body of the municipality constituting the taxing district for the refund of any tax overpaid, but without interest, and the governing body may, in its discretion, direct the return of any tax deemed by it to have been overpaid by reason of claimant's failure to make timely application for a veteran's deduction; provided, however, that no application for a veteran's deduction for any previous tax year shall be allowed by any assessor, collector or governing body. Where an application for a veteran's deduction is filed with and allowed by a collector he shall promptly transmit such application and all exhibits attached thereto, or a photostatic copy thereof, to the assessor of the taxing district. Upon receipt thereof the assessor shall review the application and if approved by him it shall have the same force as if originally filed with him.
N.J.S. § 54:4-8.13