The best method to investigate this may be synthetic controls. Researchers can use a weighted combination of similar groups (states that are like Colorado and Washington in a number of ways) to create a model of how those states might have been expected to perform with respect to crime without any changes in marijuana laws. Benjamin Hansen, a professor of economics at the University of Oregon, used this methodology to create a comparison group that most closely resembled the homicide trends and levels from 2000-12. [...] This model showed that we might have predicted more of an increase in Colorado or Washington just based on trends seen in comparable states, even without legalization. When he compared the two states with the synthetic control, Colorado and Washington actually had lower rates after legalization than you’d expect given trends. [...] Using a synthetic control approach, Mr. Hansen and colleagues showed that marijuana-related fatality rates did not increase more after legalization than what you would expect from trends and other states.
“The Reasonable Way to View Marijuana’s Risks“ from New York Times