Los Angeles has large orthodox and ultra-orthodox Jewish communities. I have, on more than one occasion, been introduced by mediation clients to the Jewish justice system - the Bet Din. I have mediated business disputes that have already been to the Bet Din and those that were destined to go there.
It is not my intention here to describe the Jewish laws requiring (or suggesting) resolution before a Bet Din, only to attach some resources here and link to others.
A "layman's guide" to Jewish Law (.pdf) (recommends mediation as one way of resolving a disputes)
The story of the stolen Torahs and the Bet Din's purported practice of "splitting the baby" below, including a blog post indicating that a Los Angeles Superior Court had been asked to confirm a Bet Din decision as an enforceable judgment.
Judge Rules against Rabbi's Widow in Torah Case reporting that the Los Angeles Superior Court has thrown out a religious court's decision to award four disputed Torahs to an Orthodox rabbi's widow who claimed that the scrolls had been stolen by her late husband's assistant.
Rabbi's Widow, LA Shul Fight Over Torah Scrolls (containing the reference to "splitting the baby")
Website for a Los Angeles Din Torah Counselor.
The London Beth Din for my British readers.
Please feel free to add to these resources.