The reason I question the assertion that poverty correlates with crime is that when I plot poverty rates for states vs homicides rates I don't see a correlation. You can check the following data for yourself. When there is a correlation the data points should more or less follow a straight line or at least a curved line. But when I plot this data I get something that looks like a shotgun blast, points all over the place. Now it would probably be more accurate to look at city level or county level data. That takes much more time than even a retired geezer would care to spend. But at least at the state level I just don't see a correlation. Let me know if you disagree.
Maybe you should look at urban vs. rural poverty. I think the correlation is much stronger between urban poverty and violent crime than rural poverty and violent crime. That explains the relatively low homicide rate relative to poverty in states like Arkansas and the Dakotas.