http://imgs.xkcd.com/comics/correlation.png

Specifically, it's possible the causation is backwards here: High-crime cities force people to be more aware and worried about crime in their city, influencing the individual's vote.  Gun policies would be a good example.  When crime is as prevalent as, for example, the crime in Detroit, voters may feel powerless to actually stop said crime without some sort of deus ex machina intervention (hence the favoritism toward liberal policies, which more often than not involve a government intervention of one form or another).  In contrast, a place like Gilbert, Arizona doesn't have much to worry about statistically in terms of crime, so from a voting perspective, crime issues are much less important and will define the politics much less.

Alternatively, the explanation could be a simple third factor influencing both statistics.  Poverty would be a good example.  Poor voters overwhelmingly vote Democrat.  Poor populations are overwhelmingly the victims and targets of violent crimes.

One thing is for certain, though.  I'm staying as far away from urban Michigan as possible.