As far as the crime type statistics go, you can use the NYPD website. The Precints that are in the South Bronx appear to be the 40th (Mott Haven), 41st (Hunts Point), and 42nd (Melrose). It of course depends on what borders you are using for "South Bronx".
This shows the stats for each precinct: http://www.nyc.gov/html/nypd/html/crime_prevention/crime_statistics.shtml
It doesn't say how many are incarcerated, but it will give you an idea.

The South Bronx looks like it's Community District 1 in the Bronx (BX CD-1)
The NYC Dept. of City Planning has stats on each Community District: http://www.nyc.gov/html/dcp/html/neigh_info/nhmap.shtml
Here is an extensive report: http://www.nyc.gov/html/dcp/pdf/lucds/bx1profile.pdf

If you still have specific questions not answered in this report, feel free to contact me directly, as I love census statistics. :-)
natalie (dot) brant (at) gmail