Here is the opinion in Bressi v. Ford, authored by Judge Canby, which is a sort of companion case to Murgia v. Reed. The court did affirm the dismissal of a Bivens-type action against the officers. Here are the lower court materials in Bressi.

An excerpt detailing what tribal officers may do during a traffic stop of non-Indians:

We conclude that a roadblock on a public right-of-way within tribal territory, established on tribal authority, is permissible only to the extent that the suspicionless stop of non-Indians is limited to the amount of time, and the nature of inquiry, that can establish whether or not they are Indians. When obvious violations, such as alcohol impairment, are found, detention on tribal authority for delivery to state officers is authorized. But inquiry going beyond Indian or non-Indian status, or including searches for evidence of crime, are not authorized on purely tribal authority in the case of non-Indians.

And an excerpt recognizing the implications of the decision:

We recognize that one result of our ruling is that tribal officers who are authorized to enforce state as well as tribal law, and proceed to exercise both powers in the operation of a roadblock, will be held to constitutional standards in establishing roadblocks. That result is consistent with our prior decision inEvans v. McKay, 869 F.2d 1341, 1348(9th Cir.1989), which held that officers acting pursuant to both tribal and city authority in making arrests were subject to a § 1983 claim. This result also appears to us to be an inevitable consequence of the accommodation of tribal authority over rights-of-way within Indian country and the rights of non-Indians to travel those rights-of-way. If a tribe wishes to avoid such constitutional restraints, its officers operating roadblocks will have to confine themselves, upon stopping non-Indians, to questioning to determine non-Indian status and to detention only for obvious violations of state law.