'Crime' is a ridiculous term, because the argument reduces to everyone is a criminal to some degree. But I think it's well established that there is a negative correlation between IQ and crime, of course not just using raw conviction rates, but after attempting to correct for factors like arrest/conviction rates.
mikerichard's point about less 'reason' to commit crime I think is a good one. A lot of crime stems from desperation.
Now I don't know about trying to create some kind of Bentham inspired calculus to put criminality on a weighted scale versus IQ and see if it all balances out.... The most terrible outliers are often economic or political leaders, by definition, their power in society gave them opportunity to commit "worse" crimes.