This is a question which essentially boils down to the nature-versus-nurture argument. In other words, is somebody prone to certain behaviors because of their genetic makeup ("nature"), or because of the environment and ways in which they were brought up ("nurture")?
Various studies have shown that children with one or more parents who have been in jail or who are currently in jail are more than twice as likely to commit crimes than children without criminal parents. This is not necessarily because of any latent genetic trait, however. It is just as likely a consequence of the social and economic conditions that those parents and their children share. Indeed, socioeconomic status always correlates negatively with most criminal behavior, and it stands to reason that a child raised in poverty is more likely to resort to criminality than a child raised in affluence.
There are, however, also studies which do link certain crimes with certain genes. A recent study in Finland, for example, isolated two genes that it claimed are linked to violent behavior, and, in a study of 900 criminals, discovered that those with these two genes were thirteen times more likely to commit violent crime than those without.
My own view on this issue is that criminal behavior can be linked to both one's nature and one's nurture. Somebody's genetic makeup, or latent traits, set certain parameters, and the same person's nurture, or socialization, will in turn determine how that person behaves within those parameters. A useful analogy is that of a car traveling on a road. The edges of the road are like the parameters set by one's genetic makeup, but the car can move slowly or quickly, in a straight line or zigzagging, according to how the driver has been taught to drive.