I believe this is more a just-so story than a fact. While New York did use the broken windows policy, they also grew the police force by 35%[1]. Rather than a special effect of the broken windows policy, it could just be with more police they were able to solve/prevent more crimes.
One interesting thing about policing in the US, is that the US has fewer police than Europe and also more crime. People want to say interesting things about how politics or culture affect crime, but the simple story (where crime is high in the US because it is relatively easy to get away with it because there aren't many police) may be the best one.