N.J. Stat. § 19:27-10.1
When a vacancy, howsoever caused, happens in the representation of this State in the House of Representatives in any year later than the 70th day prior to the day for holding the primary election for the general election but before the 70th day preceding the day of the general election, and the unexpired term to be filled exceeds one year, the Governor, in issuing a writ of election to fill such vacancy, may designate in said writ the next general election day as the day on which the election shall be held to fill such vacancy and that no primary election shall be held for nomination of candidates to fill such vacancy.
In such case, each political party shall select its candidate to fill such vacancy in the same manner prescribed in R.S. 19:13-20 for selecting candidates to fill vacancies arising among candidates nominated at primary elections, except that the time for making such selection and filing the statement thereof shall be within 10 days following the issuance of the writ of election.
In such case, petitions of nomination of other candidates shall be filed in the office of the Secretary of State within 10 days of the date of such proclamation.
The Secretary of State on the eleventh day following the date of such proclamation shall certify to the clerk and county board of each county affected by the vacancy, a statement of all candidates selected and nominated for the office so vacated.
The election to fill such vacancy shall in all other respects be conducted as though it were being conducted to fill the office upon the expiration of the term of the incumbent.
N.J.S. § 19:27-10.1