Ok quick little study of geographical breakdown in the USA.
According to a breakdown of religious belief between states published by USA today in 2002 Alabama is the most religious state with a measly 7% Non-religious population.
Washington state is the least religious state with a whopping 25% non- religious population.
By stats collected in the year 2000
Alabama ranks 20th in the overall violent crime index of the USA.
Washington is ranked 26th in the overall violent crime index of the USA.
What the study in the OP would predict is that Washington would have the least violent crime while Alabama would have the most.
This is not the case.
This totally unscientific rapid and devoid of any real study comparison would seem to provide evidence against the study in the OP.
USA Today religion by state.
Washington Crime Stats.
Alabama Crime Stats.