This article points out that this is not settled after 40 year, the jurisdictional and boundary issues of the reservation. The area of the original reservation is checker boarded with reservation land, and non reservation land. This is because of allotments being given to individuals, who then sold the property. In like fashion there are enrolled Utes, and disenfranchised Utes. So to know when you are on the reservation, and not can be very difficult. When we lived there, a federal case granted the Ute Tribe legal jurisdiction over tribal members from Fort Duchesne to Strawberry Reservoir, and in essence said all that area was the reservation. That means, where we lived, was on the reservation, although the land was not tribal land. We lived in Ballard, a couple miles from Roosevelt and a rural road to the reservation. We never had any problems with legal issues, but our baby sitters were scared once with someone being around the house.
This caused some concern, but the police handled this mostly by cross-deputization. However, it appears the issue of jurisdiction is still boiling.