Regardless of the size of any town, a county (or in Louisiana, a parish) will always have a sheriff. There's often a lot of confusion in terms. A sheriff is over an entire county, and is employed by the county, not the city. This is one of my pet peeves in movies and some books; sheriffs do NOT answer to a mayor, period. Mayors are elected to run cities, or towns. They have no authority over a sheriff, whatsoever, as the sheriff is of the county (or parish), not the city.
So, even if it's a miniscule village of 25 people, it may not have a police department, or chief of police, but there will be a sheriff, to provide law enforcement services to the entire rest of the county that particular village sits in. In Missouri, state statutes mandate that each county have a sheriff, who is in charge of a jail, civil paper service, in some cases tax collection, etc. Though I can't say definitively, I believe it's the same in every state.
There is no corresponding mandate for a police force, or chief of police. So, if a county has 18 small towns in it, none of them big enough for their own police departments or chiefs of police, there WILL still be a sheriff (and respective sheriff's agency) servicing the county, to include those small towns contained therein.
Did I vague that up enough for you?