This is a very unknown topic.......... One of the absolute last things you should do is ask a Police Officer to define a law for you, and I would not recommend asking them usually.
What I am posting here should not be construed as legal advice....... I happened to be in a class a couple years ago with a Police Officer who works on an Indian Reservation in Nebraska....... We had a discussion about this, and here was his response to me:
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Essentially, non-Native persons are subject to State law on the reservation. Tribal law is only applicable to Native Americans while they are within the exterior boundaries of the reservation. I cannot speak for other tribes, but the vast majority of the Winnebago Tribal Code directly correlates to the Nebraska Revised Statutes. Now, all persons are subject to Federal laws that are applicable.
Bear in mind that this applies to criminal law...civil jurisdictions can cross boundaries both ways.
In a nutshell, if the individual is not Native American, then he is subject to the laws of the State of Nebraska. For example, if I arrest a Native person, he is arraigned in Tribal court. If I arrest a non-Native, he is transported to the County jail and arraigned in County Court. (I am Cross Deputized) If one of our officers who is not cross-deputized come across a non-Native who needs a citation/arrest, they will contact one of us who is (if we happen to be on-duty), or the Sheriffs Office or NSP will respond.
I suppose that that was a long-winded way to say "It's not an issue!"