I’d say a lot depends on what state you live in, local law enforcement attitudes, and how crazy your neighbor is. Getting a dangerous animal complaint on record (get the neighbors to do it, too) seems like a good start if more dramatic action is required in the future.
On the other hand, being on record as complaining about the dog would make you a target of investigation and recrimination in the event authorities declined to do anything about the danger and you had to take it into your own hands to solve the problem with "more dramatic action."
If a neighbor with a pit bull repeatedly demonstrates utter disregard for the safety of the people living nearby, that neighbor is a lost cause whose emotional investment in the dog transcends common sense. I think the wiser course would be to quietly and very discreetly dispatch the dog yourself, in secret, as mercifully as possible. And when the neighbor replaced it with another pit bull (which is probably what would happen), to do it again.
My thought exactly.