"Montreal was once known as the bank robbery capital of North America."
https://montrealgazette.com/news/local-news/history-through-...
NYPD went on strike in 2014, if anyone wants to research that themselves... RIP Eric Garner
Vox did an analysis of the NYPD "slowdown"[1] as it was also a useful natural experiment. They didn't enforce the low-level "broken windows" crimes, but only did the minimum required by their contract. Needless to say, the city fared far better than right now.
That said, neither of these is a good example of what life would be life without government-supplied police forces. They are very rapid, unplanned changes in policy which don't allow private parties to hire private industry replacements and don't reflect how much less tax would be paid (about 40% of local government revenues).
[1] https://www.vox.com/2015/1/6/7501953/nypd-mayor-arrests-unio...