That isn't true: We don't police rich neighborhoods like we do poor ones, so there isn't as much opportunity to catch people doing crime, not to mention that crimes of poverty or opportunity are less when folks aren't needing to steal things. (yes, I realize that not everything people steal are things like food, but mental health is important, and things often fill these needs). In addition, poor people are more likely to get caught for some things simply because of living conditions. A decently middle class person can find a private place to smoke a joint or do drugs. Just go camping, for instance, or out in the backyard. City living plus lack of resources means you can't just go out in the courtyard of the apartments.

I'll also mention that rural places tend to have fewer cops and are seen as having a generally lower crime rate. (I didn't look up the numbers, but this is the stereotype).

A quick google suggests that evidence for a relationship between police numbers and crime rates is rather weak