I don't have any statistics to suggest that there is a correlation between gun violence and religious beliefs in the US.
However, it does seem to me that there is a correlation between "radicalism" in religion and being "gun nuts".
When I think about states that are really big on guns, I think about states like Texas etc. Republican states. These states are in the so called "bible belt". It seems to me that republicans are more likely to be radical christians. These same people are also more likely to be against stricter gun laws etc.
But, wanting to have lots of guns, or easy access to them, doesn't necessarily mean that those same people are more likely to engage in gun violence.
I do think that the correlation between radical theism and almost dogmatic adherence to the right to own weapons has deeper roots. Some kind of psychological thing that makes people more prone to black & white radical beliefs. Their belief about absolutely wanting to own (or be able to own) what I can only call war weapons, seems just as dogmatic and closed minded as their religious beliefs.
When you converse with such people about either subject, I always get the same feeling. A sense of "no matter what I say, I'll never get through to this guy...clearly he made up his mind and no amount of evidence, data or arguments is going to change that"
However, there are some correlations in the bible belt that are rather interesting....
For example, teenage pregnancy there is much higher then elsewhere. Domestic violence too.
I don't want to blame their religious beliefs for it. Because, again, correlation does not imply causation.
However, my main point here, is that US stats are the best counter argument to the ridiculous "atheism is bad cause stalin, pol pot etc".
If atheism is the reason of why the Soviet union was such a terrible place to live, then why are Sweden and Japan among the best places to live? And why then, is crime, sexual harrasment, etc so through the roof in the US compared to the rest of the western world?
That's my only point really.
I'm not blaming religion for the crime, gun violence, etc in the US.
But it does show, beyond refute imo, that the lack of religion is not what the root of the problem in Soviet Russia. If it were, then the US would be the BEST place to live. But it's not. And if it were, then Sweden and Japan would be terrible places to live. But they aren't.