Explanation:
The crime rate statistic shows the number of registered crimes divided by the number of registered residents in a country or area.
“Registered” is important here!
If you add undocumented immigrants to the calculation, the statistic is skewed:
Undocumented immigrants aren’t registered as residents for the statistic, since they are, well, undocumented.
However, any crime committed by any one of them will count towards the crime rate when they’re registered by the police.
So even if they were much less likely to commit crime than the resident population on average, the crime rate statistic would still increase. The denominator of the equation doesn’t increase by definition, because only legal residents are counted towards the statistic. But the real number of people inside the country who may commit crimes increases.
This is important to know as context when people try to “prove” immigrants are more criminal than citizens, using the crime rate statistic.
This does depend on the methodology stated by the institution collating the data. The most recent methodological statement I can find from the FBI’s stats reporting indicates it uses locality population estimates derived from the federal census - which in turn aim to count not the people each locality has registered as a resident, but the number of people who usually live and sleep in a locality regardless of documentation status.
Obviously, undocumented migrants may consciously attempt to be undercounted in that divisor but they don’t necessarily disappear entirely.
The other angle on this I’ve seen multiple times is comparisons of crime rate per capita for populations segmented by migrant status like this, where the usual conclusion is “A person is less likely to commit crime, given that they are a migrant”. It seems pretty believable to me that this reflects a raised background level of caution around crime caused by migrant status.