The high variance of crime rates across time and space is one of the oldest puzzles in the social sciences; this variance appears too high to be explained by changes in the exogenous costs and benefits of crime. We present a model where social interactions create enough covariance across individuals to explain the high cross-city variance of crime rates. This model provides an index of social interactions which suggests that the amount of social interactions is highest in petty crimes, moderate in more serious crimes, and almost negligible in murder and rape.