What is the halacha concerning joining and participating with non-Jewish courts?
It is permissible in Chutz laAretz - dina demalkhutha dina. (See TB Nedharim 28a, Gittin 10b etc). Keep in mind too that gentiles are required to establish a court system: see MT, Hilkhoth Melakhim, Chapter 9. The exception would be when two Jews have a legal wrangle. They are both hayavim to turn to a proper beth din. If one refuses, he can receive permission from the beth din to turn to a gentile court.
Friday, 03 April 2009