The answer to the problem is always construct police, courts and prisons before you even have any decent infrastructure - which is ridiculous. Most of my towns end up being populated by politically reliable felons with 70% or higher loyalty early on and half the place in or guarding the prisons! Let's just say it: The crime mode is completely broken. It's not even worth arguing about.

I constructed my first city using workers from abroad and didn't build police station, court and prison. After moving the citizens in, the criminality was not so high, but it decreased the happiness so I decided to build it. I did, criminality is under control now and everything works fine in my game. But I have to admit that I use buildings from mods that offer small police station, prisons etc., I understand that building using the vanilla buildings that are huge early in the game can be difficult.

There are small police stations, court houses, and now prisons, so justice is rather affordable even from the get go.

It is kinda spiralling but manageable.
3253 pop. I have 72 prisoners (capacity of prison is 45). Court has 7 more cases and the police offices are dealing with 5 more crimes.

I have 18326 pop and around 55 prisoners. three police stations, one court and one prison. So it is manageable, but you have to start early.

This is something I had to deal with as well. My solution was to build 3 full sized police stations and after a year in game or so things got back to normal. Then I tore one down. The small police stations don't work or are so little they don't show an affect.

Micro manage the case load as well, making sure you get a 1:1 case to police officer ratio to help get them solving more and getting criminals to jail. X out all extras that come in for a time.

Once you can get loyalty up with a TV or radio that will help as well

Hey, I noticed the "criminality" indicator in the prisons needs to be in green numbers for criminality to improve overall. So it is not just number of police stations that matters but your prisons must release "less criminous" people :)

I also am having crime issues, but only in one particular town...where my prison is. Closing in on 17k population, I've got about 200 prisoners in three locations and that one town is cracking out crime.

I've built a 3rd police station but they are so overloaded. Is the solution really to just build more police stations?

i didnt find an other way, when its already to late. On the next run a build police very soon. But in my opinion was the warning for high crime much to late for realistic mode.