Cases are unique but the question applies to all cases. If there is a conflict will you decide by secular or religious law.
It does not get anymore black and white than that.
I doubt this question comes up all that often, and probably wouldn't need a blanket ruling as I'd think any problematic case would be super specific. But I'd be shocked if there aren't numerous halachic responsa on the topic.
I am by no means an halachic expert, and would love to hear what I'm getting wrong (as I'm sure I will get plenty wrong).
In general, Halacha would only need to be adhered to if one or both parties were Jewish. Even then, in almost all civil cases, the law of land becomes the halacha. It's tough to imagine a case, even involving Jews, that would be problematic.
With non Jews, "halacha" would only be applicable in cases of the 7 Noahide laws (
https://www.chabad.org/library/article_cdo/aid/62221/jewish/The-7-Noahide-Laws-Universal-Morality.htm) one of which is establishing courts of justice, which could not enforce justice which runs counter to the other 6.
Most of those laws would not be a factor in jury cases, and for stealing and killing, I would think being on a jury would be a way of fulfilling that commandment. This may actually make jury duty an obligation, not just permisable, I'd be interested to hear how that has been addressed.
One blanket exception I would guess would be capital punishment, which I imagine no rabbi would allow someone to be party to. But all potential jurors who would vote against capital punishment are not selected for such cases, not just halacha-observant Jews.