New Jersey Statutes Title 19. Elections 19 § 27-11.2

In the case of a vacancy occurring with respect to a member of the Senate or General Assembly who was elected as the candidate of a political party which at the last preceding general election held for all members of the General Assembly received the largest number of votes or the next largest number of votes in the State for members of the General Assembly, for the interim period pending the election and qualification of a permanent successor to fill the vacancy, or for the interim period constituting the remainder of the term in the case of a vacancy occurring which cannot be filled pursuant to section 7 of this amendatory and supplementary act  1 at a general election, the vacancy shall be filled within 35 days by a member of the political party of which the person who vacated the office was the candidate at the time of his election thereto. The interim successor shall be selected by the appropriate political party's county committee or committees in the same manner prescribed in subsections a. and b. of R.S. 19:13-20 for selecting candidates to fill vacancies among candidates nominated at primary elections, and a statement of the selection of that successor shall be certified to and filed with the Secretary of State in the same manner prescribed by subsection d. of that section for certifying statements concerning the selection of such candidates.

The Secretary of State shall thereupon issue to the interim successor a certificate of selection based upon that filed statement of selection, and shall sign his name and affix the seal of the State thereto, and shall without delay deliver that statement to the person so selected. The Secretary of State shall also prepare a certified statement of selection, similar in form to the certificate but addressed to the presiding officer of the house of the Legislature in which the vacancy occurred, and shall sign the statement, affix the seal of the State thereto, and promptly deliver the same to the President of the Senate or Speaker of the General Assembly as appropriate.