If you look at the real crime statistics, you’ll notice that the crime rate started to decline well before Giuliani became mayor.
http://www.disastercenter.com/crime/nycrime.htm
That link shows the majority of the drops happening under Giuliani’s watch and increasing during the late 90’s. Also, if you compare the performance over time compared to other cities, NYC improved more than other cities, and by 2001, while other cities like chicago and San Diego were experiencing resurgence in crime, NYC continued to see crime drop.
Credit due to Giuliani.