How many people with CCW permits commit gun crimes each year?

I can't speak for the entire U.S., but in Tennessee, it's a tiny percentage. It's less than 1 percent.

Added: CCW / CWP / CPWL / Etc., laws are administered by the individual states. There is no federal input or presence in the permitting process and the statistics on WHO and HOW MANY legally carry weapons nationwide is probably not known exactly,except as an estimate.

Insofar as I am aware, when a gun-crime is committed, there is no formal collecting of data as to whether the perpetrator happened to be a permit holder or not. Overall estimates, even by anti-gun organizations, seem to reflect that, compared to the population as a wholel, it is only a very small percentage.