It can be easily shown how criminality correlates with inequality directly. Let's for example compare the homicide rates (per 100 thousand inhabitatnts per year) in 15 most equal and 15 most inequal countries in the world (measured by Gini index):

Most equal (Gini between 24.7 and 29.2)

1. Denmark 1.0
2. Japan 1.0
3. Sweden 0.89
4. Czech Rep. 1.9
5. Norway 0.60
6. Slovakia 1.7
7. Bosnia 1.8
8. Finland 2.5
9. Hungary 1.4
10. Ukraine 5.4
11. Germany 0.86
12. Slovenia 0.55
13. Croatia 1.7
14. Austria 0.55
15. Bulgaria 2.3

Most inequal (Gini between 74.3 and 53.8)

1. Namibia 18
2. Lesotho 37
3. Sierra Leone 2.6
4. Central African Rep. 30
5. Botswana 12
6. Bolivia 11
7. Haiti 22
8. Colombia 35
9. Paraguay 12
10. South Africa 34
11. Brazil 22
12. Panama 13
13. Guatemala 52
14. Chile 1.7
15. Honduras 67

The data are from Wikipedia. There may be some caveats (e.g. some countries include attempted murders in the count while others don't), but the overall correlation is easily visible.