There are a couple of problems with claiming that "CCW=less crime." To my mind, the primary problem is causation. We can measure crimes that happen in Year X, and compare it to crimes that happen in Year Y. But does that mean that CCW was the reason? It's hard to know, and many factors come into play: economics, demographics, gun issues, population density, etc. all play a role. So we need to be careful with our claims. We can say, for example, that "CCW went up M% in Year X, and crime went down N%." But can we say that "crime went down N% because of the M% increase in CCW?" Perhaps, but we have to account for as many other possible causes (thus eliminating them as operative factors) before we make that claim.
I'm a lawyer, but I'm not your lawyer. If you need some honest-to-goodness legal advice, go buy some.