43% of young men who never go to church have a record, according to the Inductivist:
The same kind of pattern holds here. For men, 43% of those who never go to church have been arrested, while only 13% of the most frequent attenders have. The corresponding percentages for females is 14% and 8%.
The results are from the GSS. The main question I would have are the affects of the background environment; in many socially conservative environments the expectation of involvement in a church is very strong and unchurched status could be a signal for anti-social tendencies. I know whereof I speak, I grew up for a while in a 3/4 Republican 99% white region of the Mountain West and those who were unchurched were often those who were “up to no good” (a small minority were secular liberals, but only a very small minority). My own prediction would be that this would be a more common phenomenon in a very religious country like the United States.