N.J. Stat. § 19:23-45
No voter shall be allowed to vote at the primary election unless his name appears in the signature copy register.
A voter who votes in a primary election of a political party or who signs and files with the municipal clerk or the county commissioner of registration a declaration that the voter desires to vote in the primary election of a political party, or who indicates on a voter registration form the voter's choice of political party affiliation and submits the form to the commissioner of registration of the county wherein the voter resides, to the employees or agents of a public agency, as defined in subsection a. of section 15 of P.L. 1974, c. 30 (C.19:31-6.3), or a voter registration agency, as defined in subsection a. of section 26 of P.L. 1994, c. 182 (C.19:31-6.11), or to the Secretary of State, either on a paper form or an electronic form using the online voter registration system established under section 1 of P.L. 2019, c. 382 (C.19:31-6.4c), shall be deemed to be a member of that party until the voter signs and files with the municipal clerk or the commissioner of registration a declaration that the voter desires to vote in the primary election of another political party at which time the voter shall be deemed to be a member of such other political party. The Secretary of State shall cause to be prepared political party affiliation declaration forms and shall provide such forms to the commissioners of registration of the several counties and to the clerks of the municipalities within such counties.
No voter, except a newly registered voter at the first primary at which the voter is eligible to vote, or a voter who has not previously voted in a primary election, may vote in a primary election of a political party unless the voter was deemed to be a member of that party on the 55th day next preceding such primary election.
Notwithstanding the provisions of this section, or any law, rule, or regulation to the contrary, a voter who is listed to receive mail-in ballots for all future elections, pursuant to the provisions of section 3 of P.L. 2009, c. 79 (C.19:63-3) or section 14 of P.L. 2018, c. 72 (C.19:63-3.1), and who is not affiliated with any political party, shall not receive a mail-in ballot for a primary election. Such unaffiliated mail-in voters shall receive a political party affiliation declaration form and information concerning how to affiliate with a political party, how to vote by mail in the primary election, and how to vote in person at a polling place on the day of a primary election. Any unaffiliated voter, who is not affiliated with any political party, may vote using a mail-in ballot in a primary election if the voter submits a political party affiliation declaration form to the municipal clerk or the county commissioner of registration and has requested or requests a mail-in ballot prior to the deadline in which a voter may apply to the county clerk for a mail-in ballot by mail pursuant to subsection b. of section 3 of P.L. 2009, c. 70 (C.19:63-3), or in person pursuant to subsection d. of section 3 of P.L. 2009, c. 79 (C.19:63-3). The Secretary of State shall cause to be prepared uniform language for such notifications. The commissioners of registration and the county clerks of the several counties and the clerks of the municipalities within such counties shall distribute such forms and information to such registered voters.
A member of the county committee of a political party and a public official or public employee holding any office or public employment to which the person has been elected or appointed as a member of a political party shall be deemed a member of such political party.
A voter may declare the voter's party affiliation or change the voter's party affiliation, or declare that the voter is unaffiliated with any party regardless of any previously declared party affiliation, by so indicating on a political party declaration form filed with the municipal clerk or the county commissioner of registration. A voter may also indicate that the voter wishes to declare a political party affiliation or that the voter does not want to declare a political party affiliation on a voter registration form filed at the time of initial registration. A voter may declare the voter's party affiliation, or make changes to that affiliation, either on a paper form or an electronic form using the online voter registration system established under section 1 of P.L. 2019, c. 382 (C.19:31-6.4c).
Any person voting in the primary ballot box of any political party in any primary election in contravention of the election law shall be guilty of a disorderly persons offense, and any person who aids or assists any such person in such violation by means of public proclamation or order, or by means of any public or private direction or suggestions, or by means of any help or assistance or cooperation, shall likewise be guilty of a disorderly persons offense.
N.J.S. § 19:23-45