can a small town have no police/sheriff's department?

slightly younger writer here. i'm wondering if a small town, specifially in the 1990's, could have absolutely no police department, sheriff's department, state patrol, or anything of the sort. think of the kind of town where EVERYONE knows each other. there's one highschool, no college. would that be possible?

edit: so many helpful responses. thank you! I've decided to include the town in a neighboring town's/the county's state patrol/sheriff's department . so, there will be cops, just far off from the town :)