Well, you are assuming a one-on-one relationship between a child in a single parent family and the commission of a crime.<quoted text>
I would expect a lag, perhaps a varying one, between the time the family became "single parent" and the time the "child" was caught committing a crime, that might make it difficult to measure.
In fact, what we are far more typically looking at is multiple risk factors. Some of these (economics, for instance) track somewhat neatly with single parenthood and others not. Some impacts may be lessoned by other family factors--a father who is present despite not being married, the presence of grandparents and other extended family, education levels, employment, a good many things.
And, of course, there is the reality of access to weapons--something a lot of folks don't like to talk about.