Crime in NYC did drop precipitously, but it's not clear that broken windows policing was the cause. It's been studied and debated a lot, but as far as I can tell there isn't a clear consensus. Here are some sources:

* https://en.wikipedia.org/wiki/Broken_windows_theory#New_York... * https://cityroom.blogs.nytimes.com/2007/08/13/why-did-crime-...