The state’s highest court will take up Mr. Baxter’s claim that a doctor’s refusal to help him die violated his rights under Montana’s Constitution — and lawyers on both sides say the chances are good that he will prevail.

Washington and Oregon allow physicians to help terminally ill people hasten their deaths, but in those states the laws were approved by voters in statewide referendums, and neither state’s highest court has examined the issue of a constitutional right to die.