I'd demand a state trooper if I was pulled over off res by tribal cops. If their stance that they are a sovereign Nation when it comes to negotiations, then as far as I'm concerned their police have no jurisdiction off that "nation's" land. I would consider it a violation of my rights to have them hold or cite and I'd challenge it as such in court. I might lose but i wouldn't just accept their law enforcement rights off res.
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Beware of the 3 inch Perch