Of course, you all know this (just as you knew immigrants are more likely to work, pay a higher proportion of earnings in tax, are less likely to be ill and don't receive as much welfare - they also have fewer children so make less use of schools) but the continuing rhetoric about immigration - migrants, refugees, asylum seekers - still talks about such folk as a problem.
Here's the evidence on crime (it's from the US - one of those nasty right wing think tanks, no less - but I don't expect it to be much different elsewhere):
Previous empirical studies of immigrant criminality generally find that immigrants do not increase local crime rates, are less likely to cause crime than their native-born peers, and are less likely to be incarcerated than native-born Americans.5 Illegal immigrant incarceration rates are not well studied; however, recent Cato Institute research based on data from the Texas Department of Public Safety found that, as a percentage of their respective populations, illegal immigrants represented 56 percent fewer criminal convictions than native-born Americans in Texas in 2015.6 The low illegal immigrant incarceration rate is consistent with other research that finds more targeting of immigrants does not reduce the crime rate, which would occur if they were more crime prone than natives.7The reality is that, almost everywhere, the net benefit from immigration is positive. Our problem is that we're full or that immigrants put massive additional strain on public services but rather that we're really bad at integrating new residents into local communities. Some of this is about racism but it's also a consequence of multiculturalism - in a society where nine out of ten people live in one culture, making a false equivalence for immigrants with a different culture won't work. And when that false equivalence becomes an obsession, the result is resentful behaviour by the majority culture.
Immigration is great but it would be even better if our expectation of immigrants was to be part of our culture not to live what Herman Ouseley called "parallel lives".