the town of 500 folks where I grew up and worked and the town of 300 where I've lived for the past 30+ years don't have a "town cop". The town of 500 did for years but it became less expensive to have the county sheriff deputies drive through regularly and respond to issues rather than employ someone fulltime maybe part time.
The small town of less than 2,000 people to my east has 3 fulltime policemen.
the rural area of the county, not counting the city of 70,000 has around 35,000 people - this area is under the Sheriff's watch. not sure how many deputies are employed, but there are 2 or 3 on patrol at all times
there are also stat highways running through the county that are patrolled by the state highway patrol
many here think it is overkill for the amount of crime and calls.
I'd guess the law enforcement numbers per capita are stronger here than in major cities, with far less crime.
bottomline is: if there is a crime reported, law enforcement will show up in a few minutes
this doesn't seem to be the case in many large cities such as Chicago