Well, I'm looking at a rather authoritative source for this sort of information -- the US Department of Justice Report on Mortality in State Prisons, 2001-2014. I don't see something listed as specifically 3.6% of inmate deaths in 2010, but can give you a rundown of causes of death that they do show in their statistics for 2010:
Cancer - 28.7%
Heart disease - 25.7%
Liver disease - 8.9%
Respiratory disease - 6.5%
AIDS-related deaths - 2.3%
Other illnesses - 16.7%
Suicide - 6.6%
Drug or alcohol intoxication - 1.2%
Accident - 1.0%
Homicide - 2.2%
Other/unknown - 0.5%
That's the information I can find for you on 2010 statistics.
