Here in Indian Territory, (most of Oklahoma), where there are no reservations like out west, the whole thing can be pretty convoluted.
Tribal police have juridiction over tribal lands and the people on them. For the most part here in Oklahoma, that means casinos. That's where all the problems are and where the vast majority calls for LE come from. Yes, there are other Tribal lands and facilities, but generally, crime happens at casinos.
If a person commits a crime on Tribal land, the incident will be investigated by Tribal law enforcement. Felony, misdemeanor alike, no difference.
If it is a major crime against persons, homicide or such, Tribal cops do call on the Feds, who here in rural OK, are generally not equipped to work a murder case. So, they in turn call on State LE who deal with this kind of case more often. A major case winds up being a joint Tribal/Federal/State effort.
If the offender is a CDIB holder, (Certificate Degree of Indian Blood), he is subject to prosecution by Tribal courts and not State courts, but may be subject to prosecution by the Federal courts, depending on the offense and the descretion of the U.S. Attorney. The U.S. Attorney may decline to prosecute in favor a State prosecution, and usually does.
If the offender on Tribal land is not a CDIB holder he is prosecuted in state court, or Federal court, depending on the nature of the offense and again, descretion of the U.S. Attorney, for the offense on Tribal land. This never made any sense to me, but that is the way it is.
That descretion of the U.S. Attorney means that they decline most cases and dump them on the State judical system.
The whole Tribal/Federal/State conundrum means as a practical matter, that in Oklahoma, the already overworked criminal justice system gets overrun by offenses created by the casinos which are a magnet for crime and criminals, but no funding, or support by Tribal governments.
So the rest of us get to pay the freight on the fabulous wealth being gleaned by Tribes from gambling, with a heavy toll to the infrastucture,(courts and jails), that cant begin to keep up.
Yea, I'm on a bit of a rant, but when I read stuff like, "another in a long series of affronts to native Americans", I kinda want to puke.
The reason our Federal cops in the local area aren't equipped to work a murder or major crime against persons? Because they spend all their time investigating corruption cases in Tribal government.