My guess is that you are asking criminally not as in family law. You may want to repost this in criminal law.
In family court anything that supports your claim of a history would work fine. Police reports, witnesses, damage reported by landlords, medical receords. But in family law we are doing so to attempt sole custody (i.e. that the parties cannot work together to make decisions regarding the child(ren)). In criminal law it is a completely different matter.