Without further adjustment, guns are not generally correlated with crime. Much talk in the gun debate exists to obfuscate this fact.
This is not to say that guns might not cause more crime/murder, all else being equal, in the context of some model. But the effect is not so large as to make guns the dominant factor in the world. If all you know about an area is how prevalent gun ownership is, you are no better at guessing its murder rate.
This page is an overview of these zero-order correlations for U.S. states.
Data on gun ownership rates by state are thin. The best survey is from the CDC BRFSS, most recently in 2001. A more recent survey, Kalesan et. al. 2015, was conducted in 2013, published in Injury Prevention, but it was smaller, and suffers from a slightly ambiguous, culturally-loaded ownership measure.
To supplement this, and bypass survey limitations, we can also look at state gun policies. From the gun rights side, I have the 2012 gun freedom rankings of the Mercatus/Cato Freedom in the 50 States report. On the gun control side, I'll use the guns laws strength rank from the 2017 Giffords Law Center scorecard.
We'll mostly be looking at UCR crime rates. For each measure, I'll compare to the closest available year (the UCR query tool doesn't provide more recent data than 2014). I considered including CDC homicide victimization rates but they were so close to the UCR rates as to be redundant.
We can also look at NCVS subnational crime estimates, 1997-2011. These are not available at the level of individual years, but bypass the police reporting chain and its possible biases.
For all of these plots, we're not interested in units, only the shape of things. Just know that:
No measure shows a relationship with murder. The Giffords ranking has a correlation bordering on significant (.245), but we can see this is driven by a couple outlier states, with no trend in the bulk of the country.
There is no relationship between guns and overall violent crime rates. All coefficients <0.15.
For context, here's what comprises the UCR violent crime index:UCR Violent Index Crime Composition
|Crime||Rate per 100,000||Percent of Total Violence|
|all violent crime||375.7||100.0%|
When we say "violent crime", we mostly mean "aggravated assault". Within this sub-category, there is no clear relationship with guns (one of four metrics was significantly positively correlated). The remaining two major components, rape and robbery, are significantly related to guns, and will be discussed separately below.
For the unfamiliar, the NCVS is a nationally-representative, survey-based crime measure that uses similar definitions to the UCR. These plots have fewer points, due to estimates being unavailable for states below two million population.
More mixed insignificant results; Kalesan closest, bordering on positively significant (.230).
One crime outcome that actually is consistently correlated to guns is robbery. Every metric I have agrees, to some extent, that more gun-owning/gun-friendly states have lower robbery rates:
Rape is the only crime outcome I've found that is positively correlated with guns. It's not as dramatic, but it's positive in most years and measures.
I don't know why this would be; rapes themselves tend not to involve weapons. It's probably some intersection of "gun culture" with, for lack of a better description, "rape culture". A pejorative explanation could be that gender-normative male cultures both like guns and commit more violence against women. A more charitable explanation may be that gun culture, particularly among women, is in part a response to the threat of sexual violence.
Why rape, and not any other category of violent crime? In both the NCVS and UCR, rape stands apart from other crime figures. While all violent crime rates are correlated with each other, rape is the least correlated with the others. I suspect it is more culturally-loaded than "regular" violence. Pondering this is beyond the scope of this article.