Some tribal law enforcement in certian tribes are granted limitted commissions by the top authority in the county the reservation is in meaning the Sheriff in that county.
That authority can be used to enforce state law on non tribal members.
Some Tribal law enforcement also have federal comissions and can enforce federal law on both Tribal members and non tribal members. This applies to felony crimes only.
Misdemenor crimes committed by non tribal members on reservation lands are subject to state laws no matter how you look at it.
BIA Law Enforcement can enforce both tribal laws and federal laws. Unless they have a limitted state comission in wich case they can enforce state laws through county courts.
I gues if a non tribal member broke a tribal ordinance or law it could be a civil issue.
Meaning if you are not a tribal member and you break a tribal odinance or law that is unique to that tribe, (meaning there is no state or federal law in place for the same thing) you can not be criminally prosecuted. Atleast I dont see how.
Maybe someone can set me straight if this is bad info.
By no means if there is a rule, law or ordinance anywhere should you break it though.
I was just trying to make it clear what laws and authorities each group is accountable to in each area with the knowedge I have.