What do you do in a case that I backed into my brother-in-law car on private property. No major damage, no dents just a little light paint on it. And my brother-in-law saids "don't worry about it, that it will go right with the other dents." And he said no police report is needed for private property. And a week later, he now wants my insurance info.

You give him your insurance info

1. depending on where ( what country and if US what state) police do not do reports on private property.
2. you should have taken a photo but that is too late now
3 he has the right to make a claim, so you either ask him how much it is and offer to write him a check instead or just give him the insurance info

I'm a liability investigator. Private property, family relationships, Police Reports do not matter.

If you damaged his property he has a right to pursue you for the repairs - that includes going through your insurance carrier.

In NY Police will write a report if the accident occurs on private property. As FrChuck said, though, this is not the case everywhere.