N.J. Stat. § 37:1-17.2
Any marriage or civil union which has occurred or which may hereafter occur and which is not recorded with the State Registrar as required by this chapter, may be recorded by filing a delayed report with the State Registrar, documented by a copy of the application for the license. The delayed report shall contain an affidavit of the person performing the marriage or civil union or if he is deceased or not available, of one or both witnesses to the marriage or civil union ceremony confirming that the ceremony was performed and the date and place of the marriage or civil union.
When it is impossible to secure the affidavit of the officiant or either of the witnesses, the affidavit may be made by a person who was present at the marriage or civil union ceremony, or the contracting parties, provided additional documentary evidence is presented.
The State Registrar may require evidence of the correctness of the information in a delayed report and may refuse to accept a delayed report if the evidence is not submitted.
N.J.S. § 37:1-17.2