There's a couple of studies on this:
Sadly, this study doesn't seem to differentiate between "rock" and "heavy metal". People who prefer "rock" have been arrested the most (13 times, but that's a fairly low number overall) and committed "arrestable" acts the third-highest, after Dance/House and Indie-fans. Check Table 16.
Adolescents who preferred heavy metal and rap music were compared with those who preferred other types of music. Results indicated that adolescents who preferred heavy metal and rap had a higher incidence of below-average school grades, school behavior problems, sexual activity, drug and alcohol use, and arrests. However, when gender was controlled, only below-average current and elementary school grades and a history of counseling in elementary school for school problems remained significant.
A longer, good write-up is Music Psychology: Heavy Metal Music.
tl;dr: Metal itself doesn't cause crimes, but adolescents with problems (who are more likely to commit crimes) are drawn to it more than adolescents without problems
This topic featured today in the newspaper (The Times, Sat Nov 17 2012, page 43). The article mentions a new survey of "the nation's metal fans" by the British Phonographic Industry with 3700 respondents.
Being a piece of journalism rather than a scientific work, the article does not give me a reference to cite, but mentions that according to the study the average metal fan is "more sporty, sociable and musical than fans of other genres ... highly educated" and that metal "is seen as a positive force in the lives of those who listen to it".
I mention this in case anyone is interested in tracking down the original survey; the Times article itself is only available online behind a paywall (http://www.thetimes.co.uk/tto/arts/music/article3603301.ece).