N.J. Stat. Ann. § 16:12-7

When a vacancy shall occur in the office of rector, in any manner whatsoever, the wardens and vestrymembers, two-thirds of them concurring in the choice, may, subject to the constitution and canons of the Protestant Episcopal Church in the United States, and of the diocese in which the parish is located, choose some fit person, duly qualified, to be rector of the parish.