Virtually every study done points to the fact the immigrants, even illegal immigrants, are less prone to crime than American citizens. That is why immigration opponents must rely on repetition of lurid single examples to try to make their case, a bit like global warming advocates point to individual heat waves as a substitute for having any warming show up in the recent global temperature metrics.
With few exceptions, immigrants are less crime prone than natives or have no effect on crime rates. As described below, the research is fairly one-sided.
There are two broad types of studies that investigate immigrant criminality. The first type uses Census and American Community Survey (ACS) data from the institutionalized population and broadly concludes that immigrants are less crime prone than the native-born population. It is important to note that immigrants convicted of crimes serve their sentences before being deported with few exceptions.
However, there are some potential problems with Census-based studies that could lead to inaccurate results. That’s where the second type of study comes in. The second type is a macro level analysis to judge the impact of immigration on crime rates, generally finding that increased immigration does not increase crime and sometimes even causes crime rates to fall.
Butcher and Piehl examine the incarceration rates for men aged 18-40 in the 1980, 1990, and 2000 Censuses. In each year, immigrants are less likely to be incarcerated than natives with the gap widening each decade. By 2000, immigrants have incarceration rates that are one-fifth those of the native-born
There is a lot more at the link.