It differs by jurisdiction. The jurisdiction is the location of the wedding. Because we got married in Cranston, we contacted Cranston City Hall with this question.
No, there is a state law that governs this, and JOPs are not allowed to perform marriages unless they are also one of the types of judges, magistrates, clerks of the court, etc. named in the state law:
Re: Who can perform a wedding ceremony in RI?
Clergy members also can officiate, of course.