Genetic variations in MAOA (monoamine oxidase-A) have been shown to be linked to increased levels of risk-taking behaviour, as well as being linked to increased aggression levels. So that's clearly one possible genetic link.
Further, there seems to be considerable evidence that some forms of autism are inherited. (I'm on the autism spectrum, as clearly was my father and his brother, with them almost certainly having inherited their autism from their father). Autism can result in people not really caring about others, or bonding with them. That can have benefits, as people with high-functioning autism often excel in the so-called 'caring' professions, precisely because they can stand back from situations and not get perrsonally involved. (e.g. a paramedic who regards his work as 'just a job' is probably far more efficient than someone who feels deeply for casualties). Conversely though, it can mean that they're more likely to commit crimes (especially sexual ones) because they're unable to see things from the point of view of their victims.
So genetics may definitely have some influence over whether people do, or don't, commit crimes. However that's not to say that environmental factors might not be far more important.