Sure. But since income disparity has soared in the last 40 years and crime rates have plummeted, even if they have plummeted everywhere, this indicates that inequality, if it has any effect at all, is likely pretty minor.
I think this would be near impossible to test for though. So many factors affect crime rates across difference societies, and different societies experience wildly different types of income disparity. Intuitively, I imagine places with smaller net income disparity but larger real income disparity (ie a city where everyone is relatively poor but some are destitute) have much more crime than places with larger net income disparity but smaller real income disparity (ie a city where everyone is relatively wealthy, but a few are unbelievably rich).
I think this would be near impossible to test for though. So many factors affect crime rates across difference societies, and different societies experience wildly different types of income disparity. Intuitively, I imagine places with smaller net income disparity but larger real income disparity (ie a city where everyone is relatively poor but some are destitute) have much more crime than places with larger net income disparity but smaller real income disparity (ie a city where everyone is relatively wealthy, but a few are unbelievably rich).