Who does the selection? In the USA, doesn’t it always come down to voter choice one way or another? We typically elect a sheriff but a mayor appoints a police chief. The mayor is elected however. What process could be used to determine process and selection that would avoid voter input?
Appointment by mayor or local government is fine. Make it a normal public service job. There are reasonable questions about why the US needs quite so many fine-grained local police authorities and who polices the police, though.
Make them fight to the death? Seriously, it would solve sooo many problems.
Open application process. Select whoever had the highest law school grades. Or alternatively make all the applicants take a competitive exam. Anonymous grading.