From where I sit, I can tell you that, while there are certain crimes where it is common to have an illegal perp, in the case of the truly bad crimes (murder, rape) it aint the illegals doing it, at least not in Jersey.
I can’t speak for New Jersey, but illegals cause a huge amount of crime. They are big into drunk driving, theft, drugs, burglary, tax evasion...Stuff like that, and don’t be fooled, they do drive murder rates up.