Cities crime rates have little to do with their local politics. Giuliani for example got a great deal of praise for lowering crime in NYC but wildly different approaches also seemed to “work” in other cities.
Look at a graph of murder rates for LA vs NYC and their surprisingly similar even with very different politics. https://www.nytimes.com/interactive/2016/05/18/us/chicago-mu...
Chicago, NYC, LA, and many other US cities all had similar trends over similar time periods which line up with national trends. https://www.macrotrends.net/countries/USA/united-states/murd...