There is a recent 2013 paper on this topic by Andrew Beauchamp and Stacey Chan, the abstract is here:
Does crime respond to changes in the minimum wage? A growing body of empirical evidence indicates that increases in the minimum wage have a displacement effect on low-skilled workers. Economic reasoning provides the possibility that disemployment may cause youth to substitute from legal work to crime. However, there is also the countervailing effect of a higher wage raising the opportunity cost of crime for those who remain employed. We use the National Longitudinal Survey of Youth 1997 cohort to measure the effect of increases in the minimum wage on self-reported criminal activity and examine employment–crime substitution. Exploiting changes in state and federal minimum wage laws from 1997 to 2010, we find that workers who are affected by a change in the minimum wage are more likely to commit crime, become idle, and lose employment. Individuals experiencing a binding minimum wage change were more likely to commit crime and work only part time. Analyzing heterogeneity shows those with past criminal connections are especially likely to see decreased employment and increased crime following a policy change, suggesting that reduced employment effects dominate any wage effects. The findings have implications for policy regarding both the low-wage labor market and efforts to deter criminal activity.
For the pointer I thank Kevin Lewis. And there is an ungated version here (pdf). And via Gordon, here is a profile behind one of the forces behind the campaign to raise the minimum wage. Here is a good recent article on minimum wages and cross-state mobility.