It's hard to show directionality in some locales, but the correlation can be interesting.

For example when I transferred to DC about 10 years ago, I checked the FBI crime stats for DC, Arlington county, VA and Montgomery and Prince Georges counties in MD as I decided where I was going to live.

In DC, where gun ownership was rare and concealed carry unheard of, the murder rate was 21 per 100,000. In MD, where gun ownership was legal, but concealed carry uncommon as permits are very hard to get, the murder rate was 14 per 100,000. Finally, in Arlington county where concealed carry permits were available on a "shall issue" basis, the murder rate fell to 7 per 100,000.

A few years later I took some concealed carry permit paperwork into a DC branch of my bank to get notarized. I was surprised that the banker that took care of it for me, an otherwise fairly liberal guy, ranted for 15 minutes about DC's refusal to issue permits. He cited the frequency of individuals from MD and VA coming into the Columbia Heights and Adams Morgan neighborhoods and mugging people because it was guaranteed they would be unarmed. He also cited the inability to safely use any of the bike or jogging trails for the same reason.

Putting the two together, you could conclude that the correlation between the concealed carry, gun ownership and the murder rate may have some directionality, even when all the other confounding variables are considered.

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In general, I've observed that an armed society tends to be a polite society. If people choosing to conceal carry do so because of a misperception of high crime, but it also serves as a deterrent against crime then there isn't a downside.