I found this online for what it’s worth:
I am dealing with jury duty at the moment. What is the halacha concerning joining and participating with non jewish courts?
Warmest Regards,
Hillel
It is permissible in Huss laAress – 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.