Dalrymple comments on a recent study in the New England Journal of Medicine addressing the above question:

The authors draw attention to the fact that since 2005 more than 150 people in Michigan with licences to carry concealed weapons have committed suicide and in a 5 year period in North Carolina 2400 permit holders were convicted of crimes, including 900 drunk driving offences and more than 200 felonies. This is supposed to demonstrate that doctors have no particular skill in assessing the competence of their patients to carry concealed weapons, which may well be the case (I rather suspect that it is), but these raw figures prove nothing very much. As is all too often the way, they provide numerators which shock but no denominators which soothe or reassure. Nor is there any standard of comparison: it might be, for example (though I rather doubt it), that people with licences in Michigan are less likely to commit suicide than an equivalent number of people of similar demographic characteristics without licences. The connection between gun licences and suicide might not be a causative one; and even if it were, it would still need to be shown that the type of people who have a concealed gun licence and commit suicide are more likely to commit crimes with guns than they would otherwise be. For it is specifically gun crime that licensing is supposed to control, not suicide, drunken driving or all felonies as such.