N.J. Stat. § 19:3-5
No person shall hold at the same time more than one of the following offices: elector of President and Vice-President of the United States, member of the United States Senate, member of the House of Representatives of the United States, member of the Senate or of the General Assembly of this State, county clerk, register, surrogate or sheriff.
No person shall hold the office of member of the Senate or the General Assembly of this State and, at the same time, hold any other elective public office in this State, except that any person who holds the office of member of the Senate or the General Assembly and, at the same time, holds any other elective public office on the effective date of P.L. 2007, c. 161 may continue to hold that office of member of the Senate or that office of member of the General Assembly, and may hold that other elective public office at the same time if service in the Senate or the General Assembly and the other elective office are continuous following the effective date of P.L. 2007, c. 161.
No person shall be elected an elector of President and Vice-President of the United States unless he shall possess the qualifications of a legal voter of the State, shall be of the age of 25 years or upwards and shall have been a citizen of the United States seven years next preceding such election.
No person shall be elected a member of the House of Representatives, or an elector of President and Vice-President who shall hold any office of trust or profit under the United States.
N.J.S. § 19:3-5