My job involves a lot of contact with prisoners. I'm not aware of any empirical studies of how class intersects with incarceration. Anecdotally speaking, however, I can tell you that the vast majority of prisoners I've dealt with have stuck me as coming from pretty impoverished backgrounds.
The NC DOC website allows you to run statistical reports. http://www.doc.state.nc.us/rap/index.htm
I ran a simple report for the 2007 prison population grouped by race only. In 2007, the NC prison system had 13,367 white inmates and 22,049 black inmates. That's a pretty astounding when you consider that NC is about 22% black . Based on my experience, I'd put 100 bucks on the white/black ratio not changing much if you only counted "poor" blacks and whites. And even if it did, I doubt the white/black ratio would closely mirror the white/black ratio of poor people in NC.
-WD