I’ve mentioned in the past that Louisiana and Ohio are the only remaining states that have “Mayor’s Courts” named as such, however some states do allow mayors to sit as judges in courts using different names, among them South Carolina’s Municipal Courts under 5-7-90:
The mayor or municipal judge or judges of any municipality shall speedily try all persons charged with violations of the ordinances of the municipality or the laws of the State within their jurisdiction in a summary manner without a jury unless jury trial is demanded by the accused.
That will soon end however as the state’s governor has signed into law yesterday HB 4798. When introduced the bill dealt with how long a person could be held pending trial (currently 7 days). The bill extends that to 10 days, but a committee amendment also struck out the provision allowing mayors to sit as trial judges.