This esoteric exercise takes on real world implications when Congressional districts are drawn or funding formulas calculate who gets what money based on population projectsion - big cities where most prisonsers come from lose out, while rural jurisdictions where most prisons are get extra resources to manage a phantom group for whom they provide no services. The simple solution to the problem would be to count prisoners from the county they came from, not where they're incarcerated.
Here are the stats for a few Texas counties to show how their minority population statistics in the Census are skewed by prisons operating in their jurisdictions. Some of these are tiny places reporting signficant minority populations. Keep in mind that whenever you see exorbitant numbers in rural counties, larger cities are being equally undercounted.
counties' minority residents under 2000 census
There's quite a bit of interesting information here, including individual profiles of counties with the highest prisoner populations like Anderson or Walker.
Maybe more later, but for now check out the tool - they've got information available for jurisdictions nationwide. But of course, why would you care about anywhere but Texas? ;-)