Federal law prohibits gun purchases by an "unlawful user and/or an addict of any controlled substance." In 2011, the Bureau of Alcohol, Tobacco and Firearms clarified in a letter that the law applies to marijuana users "regardless of whether [their] State has passed legislation authorizing marijuana use for medicinal purposes." Though a growing number of states are legalizing it for medical or recreational use, marijuana remains illegal for any purpose under federal law, which considers the drug to have a high potential for abuse and no accepted medical use.

The U.S. Circuit Court of Appeals for the 9th Circuit ruled that the federal law passes muster with the Constitution, as "it is beyond dispute that illegal drug users, including marijuana users, are likely as a consequence of that use to experience altered or impaired mental states that affect their judgment and that can lead to irrational or unpredictable behavior."

The court then concluded that it is reasonable to assume that a medical marijuana cardholder is a marijuana user, and hence reasonable to deny their gun purchase on those grounds.

From a legal standpoint, the nexus between marijuana use and violence was established by the U.S. Court of Appeals for the 4th Circuit in Virginia, in the 2014 case of United States v. Carter. That case cited a number of studies suggesting "a significant link between drug use, including marijuana use, and violence," according to the 9th Circuit's summary.

In the words of the 4th Circuit, those studies found that:

The 4th Circuit argued that, on the link between drug use and violence, the question of correlation vs. causation doesn't matter: "Government need not prove a causal link between drug use and violence" to block firearms purchases by drug users. A simple link between drug use and violence, regardless of which way the causality runs, is grounds enough.

Still, the 9th Circuit did suggest causation was part of its decision, saying that irrational behavior can be "a consequence" of marijuana use.

This argument — that substance use increases risky behavior — applies to plenty of other drugs, too, and not just illegal ones. For instance, drug policy researchers Mark Kleiman, Jonathan Caulkins and Angela Hawken have pointed out that tobacco users also are more likely to engage in crime relative to the general population.

The authors also point out that there's a much stronger link between violent behavior and alcohol than there is for many illegal drugs: "There is a good deal of evidence showing an association between alcohol intoxication and pharmacologically induced violent crime," they write.