The author did publish a peer-reviewed article in 2009 discussing the issue, with sources. I've verified most of the sources and they seem to be reliable and reputable.
Criminality and Moral Conduct
In many people’s minds – and as expressed so clearly in Psalm 14 cited at the outset of
this essay – atheism is equated with lawlessness and wickedness, while religion is equated with morality and law-abiding behavior. Does social science support this position?
Although some studies have found that religion does inhibit criminal behavior (Baier
and Wright 2001; Powell 1997; Bainbridge 1989; Elifson et al. 1983; Peek et al. 1985)
others have actually found that religiosity does not have a significant effect on inhibiting criminal behavior (Cochran et al. 1994; Evans et al. 1996; Hood et al. 1996). ‘‘The claim that atheists are somehow more likely to be immoral,’’ asserts Benjamin Beit-Hallahmi (2007, 306), ‘‘has long been disproven by systematic studies.’’
Admittedly, when it comes to underage alcohol consumption or illegal drug use,
secular people do break the law more than religious people (Benson 1992; Gorsuch
1995; Hood et al. 1996; Stark and Bainbridge 1996). But when it comes to more serious
or violent crimes, such as murder, there is simply no evidence suggesting that
atheist and secular people are more likely to commit such crimes than religious people.
After all, America’s bulging prisons are not full of atheists; according to Golumbaski
(1997), only 0.2 percent of prisoners in the USA are atheists – a major underrepresentation.
If religion, prayer, or God-belief hindered criminal behavior, and secularity or atheism fostered lawlessness, we would expect to find the most religious nations having the lowest murder rates and the least religious nations having the highest. But we find just the opposite.
Murder rates are actually lower in more secular nations and higher in more religious
nations where belief in God is deep and widespread (Jensen 2006; Paul 2005; Fajnzylber
et al. 2002; Fox and Levin 2000). And within America, the states with the highest murder
rates tend to be highly religious, such as Louisiana and Alabama, but the states with
the lowest murder rates tend to be among the least religious in the country, such as Vermont and Oregon (Ellison et al. 2003; Death Penalty Information Center, 2008). Furthermore, although there are some notable exceptions, rates of most violent crimes tend to be lower in the less religious states and higher in the most religious states (United States Census Bureau, 2006). Finally, of the top 50 safest cities in the world, nearly all are in relatively non-religious countries, and of the eight cities within the United States that make the safest-city list, nearly all are located in the least religious regions of the country (Mercer Survey, 2008).
Atheism, Secularity, and Well-Being: How the Findings of Social Science Counter Negative Stereotypes and Assumptions, Phil Zuckerman, Sociology Compass 3/6 (2009): 949–971, 10.1111/j.1751-9020.2009.00247.x
In short, his argument is as follows:
There's tons of studies, but a lot of contradictions.
We can say with certainty that religion is a good influence on drug use and other "vicimless" crimes -- they are called "anti-ascetic" crimes in the literature I've read.
There is no clear signal that religion inhibits violent crimes (there are many articles disagreeing with each other, lots of discussion about confounding factors, questionable methodologies, etc.)
Atheists are majorly underrepresented in prisons, although of course this doesn't prove the point, but certainly disproves that atheism causes criminal behavior.
There's a negative correlation between large scale atheism and crime.
More secular countries have lower violent crime rates.
More secular US states have the lowest violent crime rates, more religious US state the highest.
The safest cities are either in less-religious countries or when in the US they are in less-religious states.
My personal opinion is that many of these studies tend to be poorly constructed. For example many studies on crime rely on objectionable proxy variables which are then contested by other studies. Is reporting that "one doesn't trust policemen" a reliable indicator of delinquency? Is religious literacy a good proxy for religiousness?
This particular article attempts to put together what we know about the subject of atheism, but of course its argument can't be stronger than its sources.