The Michigan Supreme Court issued an order adopting a new rule for judicial disqualification earlier this week (late afternoon on Thanksgiving eve, as one dissenting justice notes). The rule explicitly incorporates the recent U.S. Supreme Court decision Caperton v. Massey, and it establishes a process for the justices to disqualify each other. If you have the time, the concurring and dissenting opinions in the order are spirited and well worth the read. Or you can catch the highlights from the press coverage: "Divisions easy to read in new Mich. court rule" and "New Michigan Supreme Court rule will let judges toss one of their own."
Michigan, however, is not the first to adjust recusal standards post-Caperton. The Wisconsin Supreme Court did so in late October, as summarized here.