You can look up the NYPD report on crime for the month of june the total amount of reported crime was 427 for all forms of transport (metro, bus, etc). 3.6 million people use public transport in NYC daily.

No matter where you are, you'll never drive that number to 0. But if you wanted to make it better then you'd stop positioning the police to catch turnstile jumpers and you start positioning police to ride public transport during low ridership times to prevent incident.