The NYPD release monthly crime totals at the precinct level, recent statistics are available for felony crimes (murder, rape, robbery, felony assault, burglary, grand larceny, and grand larceny auto) for individual precincts as are historical tables from 2000.
Incident level statistics, including misdemeanors and violations, are now available. Records and locations of complaint data from 2006 are on NYC OpenData, the most recent year is here. GIS files for complaint data are available from Geodata@Columbia.
For GIS users, precinct level felony data since 2000 is available in spatial formats through GeoData@Columbia.