Certainly drug abuse leads to some crime. The research indicates that a large percentage of arrested persons are under the influence of drugs and/or alcholol at the time of their arrest. Of course, it could be argued that being under the influence just makes them easier to spot and therefore more likely to be arrested that criminals who aren't high.
For a good look at the 13 major theories of why people commit crime, here is a webpage with a download to a criminological theory crib sheet. Which of the major theories supports your statement?
