Joseph- I know they shouldn’t but from what I’ve heard some if them do. Maybe bc they are scared the civil court will overturn their ruling if one of the parties isn’t happy with the psak. For whatever reason people have told me it’s done that way. If someone then doesn’t listen to the beis din they can be put into cherem or whatever the beis din does to people who don’t listen.
Can’t the beis din also claim Dina dmalchusa?