Details are still emerging about Aaron Alexis, the 34-year-old ex-Navy officer who allegedly killed 12 people on Monday at Washington’s Navy Yard.

Records indicate that Alexis had been suffering from “a host of serious mental issues, including paranoia and a sleep disorder” and reported hearing “voices in his head.” He was involved in at least two incidents involving a gun and in January of 2011 received a discharge from the Navy.

But if “a pattern of misconduct” was enough to end Alexis’ military career, what would it take to prohibit him from legally carrying a gun?

A new study called “License To Kill” out today from the Center for American Progress tries to answer that question by examining how states regulate concealed carry permits. News reports indicate that Alexis received a concealed carry permit from Texas and purchased a shotgun in Virginia.

Federal law prohibits felons, domestic abusers, the mentally ill, and other broad categories of individuals from receiving concealed carry licenses. Many states ban additional categories of people — those who commit misdemeanors or have a demonstrated history of alcohol- or substance-abuse problems — from carrying guns, and two dozen states grant local officials varying degrees of discretion in denying concealed carry permits. In those jurisdictions, for instance, prior arrests and a history of violence could lead to a denial of application for a concealed carry permit.

Arkansas, Montana, and Utah, the CAP report notes, could deny applications to individuals with “past patterns of behavior or participation in an incident involving unlawful violence” that would make it “reasonably likely” that they could pose risk to the community.

In 10 states, authorities can “look more deeply into whether the individual possesses the high level of moral character required to be entrusted with the responsibility of carrying and, in some states, whether they have a demonstrated need to carry a firearm.”

Texas, however, is a “shall-issue” state. The Texas Department of Public Safety must issue a concealed handgun license if the applicant meets certain qualifications. Texas does prohibit carrying for some misdemeanants convicted within 10 years, but is one of 21 states that don’t grant authorities discretion in granting permits.

Texas law also “requires the Governor of Texas to negotiate agreements with other states that issue concealed handgun licenses so that Texas may recognize such licenses.” Virginia, where Alexis may have purchased a weapon used in the shooting, has a written agreement with Texas, requiring the state to honor Texas’ licenses.

For years, the National Rifle Association has worked to establish national gun reciprocity, advocating for a new federal mandate that would override existing state laws and allow anyone with a concealed gun carry permit issued by one state to carry guns into any other state. In April, the measure received 57 votes in the Senate, one more than an amendment expanding background checks. Both fell short of the 60-vote threshold, however.

The District of Columbia has some of the toughest gun laws in the country, but it is a victim of lax gun laws elsewhere. A 2010 report from Mayors Against Illegal Guns, finds that 98.2 percent of all guns used for crime in the District come from states with weaker gun laws, including Virginia.