Unfortunately it would be hard to prove and even if it could be the mainstream media/liberals would never let the word get out.
It's actually impossible to prove. Spats is correct: causation is the issue.
Atlanta has very high rates of violent crime across most categories, but it's in a very permissive state. On the other hand, Giuliani slashed crime rates in New York without doing anything to remove their draconian laws. There are simply too many variables in economics, policing, and demographics to boil things down to one factor.
Statistics can be manipulated, and they can be used to "prove" either side of the argument. This is my main problem with this line of argument. Arguing from the standpoint of social utility is a time-tested tool for the other side, and they've got more practice than we do.
The one thing I think it is safe to infer is that more guns and liberalized CCW do not increase crime