I also agree with everyone that posted here that no member of the blood Corleone family would ever use the judicial system. But, to be more clear, no Corleone would use the judicial system at that time. Later, in GFIII, Michael famously says, "I need more lawyers." In Michael's quest for legitimacy (however "real" that quest actually was), he had to bend and accept the democratic way of the corporate world.

In short, it was a matter of goals.
In GF1, the goal was the immediate safety of Vito and the survival of the family.
In GF3, the goal was being considered legit in the eyes of the public (at least, so says Michael).