N.J. Stat. § 19:23-13
Should any person indorsed in any petition as a candidate to be voted for at any primary election, except for the office of "Choice for President," delegates and alternates to national conventions, Governor, United States Senator, member of the House of Representatives, State Senator, members of the General Assembly, and any county office, die within three days after the last day for filing such petition, or in writing filed within three days after the last day for filing such petition with the county clerk or municipal clerk with whom such petition had been filed, decline to stand as a candidate, the vacancy or vacancies thus caused shall be filled by a majority of the persons signing the petition in and by which the person so dying or declining was indorsed, filing within three days after the occurrence of the vacancy with the municipal clerk, a new petition, setting forth the name of the person dying or declining the office for which he was indorsed, and the name of the person to be substituted, to which shall be annexed the oath of allegiance prescribed in section 41:1-1 of the Revised Statutes duly taken and subscribed by the person so nominated before an officer authorized to take oaths in this State.
Such petition shall be verified by three of the signers, and shall have the same force and effect as the original petition.
N.J.S. § 19:23-13