"In sum, these findings run counter to arguments suggesting the legalization of marijuana for medical purposes poses a danger to public health in terms of exposure to violent crime and property crimes. To be sure, medical marijuana laws were not found to have a crime exacerbating effect on any of the seven crime types. On the contrary, our findings indicated that MML precedes a reduction in homicide and assault. While it is important to remain cautious when interpreting these findings as evidence that MML reduces crime, these results do fall in line with recent evidence  and they conform to the longstanding notion that marijuana legalization may lead to a reduction in alcohol use due to individuals substituting marijuana for alcohol [see generally 29, 30]. Given the relationship between alcohol and violent crime , it may turn out that substituting marijuana for alcohol leads to minor reductions in violent crimes that can be detected at the state level. That said, it also remains possible that these associations are statistical artifacts (recall that only the homicide effect holds up when a Bonferroni correction is made)."
Robert G. Morris, Michael TenEyck, JC Barnes, and Tomislav V. Kovandzic, "The Effect of Medical Marijuana Laws On Crime: Evidence From State Panel Data, 1990-2006," PLoS ONE 9(3): e92816. March 2014. doi: 10.1371/journal.pone.0092816.