N.J. Stat. § 19:23-26.1
In the case of a primary election for the nomination of a candidate for the office of United States Senator and in the case of a primary election for the nomination of a candidate for the office of Governor, the names of all candidates for the office of United States Senator or Governor shall be printed on the official primary ballot in the first column or horizontal row designated for the party of those candidates.
In the event that the nomination of candidates for both offices shall occur at the same primary election, the names of all candidates for the office of United States Senator shall be printed in the first column or horizontal row designated for the party of those candidates, and the names of all candidates for the office of Governor shall be printed in the second column or horizontal row.
No candidate for nomination for any other office shall have his name printed in the same column or horizontal row as the candidates for nomination for the office of United States Senator or Governor.
N.J.S. § 19:23-26.1