https://www.cnn.com/2018/11/03/us/immigrants-crime-numbers/index.html

One interesting one from the Conservative side:

'719
The criminal conviction rate per 100,000 immigrants in Texas. This number comes from a study by the Cato Institute, which uses figures from Texas in 2015 as a case study to look at how crime rates compare among immigrant and native-born populations.
"The criminal conviction and arrest rates for immigrants were well below those of native-born Americans," Cato's Alex Nowrasteh wrote.
According to the libertarian think tank's analysis, the rate per 100,000 residents in each subpopulation was 899 for undocumented immigrants, 611 for legal immigrants and 1,797 for native-born Americans.'

So an illegal might be slightly more likely to commit a crime than a legal immigrant, but FAR less than a native-born American.

Interesting.