Americans who claim a religion are less criminal: The General Social Survey asked more than 9,000 respondents if they had a religion and whether they have ever been arrested. Here are the percent ever having been arrested:
Percent ever arrested
No religion 25.0
No religion 28.6
No religion 54.5
People with no religious affiliation are a lot more likely to have been arrested, especially Mexicans (caution: non-affiliated Mexican sample is small--11). It's interesting how black Catholics, unlike for other ethnic groups, are much worse than they're Protestant counterparts. Later, I'll try to find evidence to explain this.
Of course, a correlation between naming a denomination and obeying the law does not prove that religion has a salutary influence on behavior: it might be that morally inclined people both claim a church and avoid crime. The most we can say is that these numbers support the thesis that religion improves behavior.
Part of the "no religion" group is made up of intelligent, skeptical people who have qualities making them unlikely candidates for a career in crime. If we removed them, I imagine the arrest rates of the rest would be even higher.