Here's an interesting question: Are law enforcement officers who work for native american tribes regulated by the Fourth Amendment? Are they state actors for constitutional purposes? My understanding from a few cases is that the answer is technically no, but in practice yes. /1`
Here's an overview of the law from the Supreme Court of South Dakota. scholar.google.com/scholar_case?c… 
Put another way, the statute, the Indian Civil Rights Act, requires officials of the tribes to follow the Fourth Amendment.
There's an interesting question of whether the statute tracks changes in constitutional doctrine: The statute was enacted in 1968, did it lock in 4A law as of then? But my sense is that courts treat it as enacting by statute whatever 4A law is now.
