From Politifact:

Arizona Republican Gov. Jan Brewer created a frenzy in April 2010 when she signed a law that makes being an illegal immigrant a state crime and requires legal immigrants to carry papers that confirm their status. Then in late June, she linked illegal immigrants and drug smuggling.... On the broader issue, it's worth noting that statistics have consistently shown that immigrants, including illegal immigrants, actually have lower rates of criminal activity and incarceration than do the native-born children of immigrants. Rubén G. Rumbaut, a sociologist at the University of California, Irvine, has written that 2000 Census figures show consistently lower incarceration rates for foreign-born Mexicans, Salvadorans, Guatemalans, Colombians, Ecuadorians and Peruvians when compared to incarceration rates of U.S.-born members of the same ethnic groups. While the category "foreign-born" is not identical to "illegal immigrant," there is significant overlap in these particular ethnic groups, Rumbaut writes.

For the full story, please visit http://www.politifact.com/truth-o-meter/statements/2010/jun/30/jan-brewe....