The town of Mythic Wood has no police force of its own, relying instead on the Coos County Sheriff's Department to enforce the law. There is a Sheriff's Office in town, run by a Chief Deputy. The actual Coos County Sheriff rarely appears in Mythic Wood.
The Sheriff's Office has jurisdiction over the entire town of Mythic Wood and the surrounding territory, except for the Reservation. At least, that's what the law states. The truth is more complex.
The mobile home park on the west side of the city is run by the Iron Brigade. While no law grants them jurisdiction there, the town government and the Sheriff's Office realize that an attempt to force the issue would lead to a dangerous conflict. The IBMC is essentially the local militia, and they have the manpower and firepower to back up that claim.
The Lestrange Family and the Celestial Dusk, to the east, consider their territory a sovereign nation, and its residents will violently defend their territory against incursions of almost any kind. Unfortunately, just what territory the Lestranges and their followers consider theirs isn't entirely clear, which has led to a number of conflicts.
The lead position in the local Sheriff's Office is the Chief Deputy. All other officers are Deputy Sheriffs, typically just referred to as Deputies. Though there are no ranks distinguishing between Deputies, there is certainly a pecking order, typically based on seniority.