There is an interesting article on immigration and crime here, in a magazine not notably supportive of immigration, which pretty much debunks the notion that Mexican immigrants to the United States have significantly higher rates of crime than white Americans, despite Mexico's high levels of violence at the moment.
It also demonstrates that Hispanics is a bit of a phony category (not as bad as "Asian Pacific Islanders") in that different Hispanic groups Mexicans, Cubans, Puerto Ricans & Domincans have very little in common.
In fact "immigrants" as a whole shouldn't really be considered as one amophous group. As my post of last year on the different imprisonment rates for different nationalities in England & Wales demonstrated some immigrant groups have higher rates than the domestic population and some have lower rates. There isn't a generic immigrant crime rate.