Shulchan Aruch(C.M. 26:1): It is prohibited to have a non‑Jewish court make judgments in a dispute between Jews. This is so even if they make judgments based on Jewish law and even if the litigants agree to accept their judgment. Who ever used the non‑Jewish court is a rasha (wicked person). It is as if he has denigrated the Torah of Moshe. Rema: The Jewish court has the right to excommunicate and ostracize those who utilize the authority of non‑Jews. Similarly there can be various punishments enacted against someone who goes to a non‑Jewish court – until they retract….
Shulchan Aruch(C.M. 26:2): If the non‑Jews are the controlling power and the litigant is powerful in his own right and therefore the person can not recover what is his by the authority of the Jewish court – he should first summon his opponent to the Jewish court. If his opponent refuses to go – he should obtain permission from the Jewish court and then use the non‑Jewish court to recover what is his from his opponent. Rema: The Jewish court has the right to go to the non‑Jewish court and to testify that one person owes the other money. All this is only if one of the litigants refuses to obey the Jewish court. Otherwise it is prohibited for a Jewish court to give authorization for Jews to have their dispute presented to a non‑Jewish court