Mich. Comp. Laws § 205.602
In any case in which this state and 1 or more other states each claims that it was the domicile of a decedent at his death, at any time prior to the commencement of legal action for determination of domicile within this state or within 60 days thereafter, any executor, or the taxing official of any such state, may elect to invoke the provisions of this act. Such executor or taxing official shall send a notice of such election by registered mail, receipt requested, to the taxing official of each such state and to each executor, ancillary administrator, and interested person. Within 40 days after the receipt of such notice of election any executor may reject such election by sending a notice, by registered mail, receipt requested, to all persons originally required to be sent a notice of election. When an election has been rejected by an executor, no further proceedings shall be had under this act. If such election is not rejected within the 40-day period, the dispute as to death taxes shall be determined solely as hereinafter provided. No other proceedings to determine or assess such death taxes shall thereafter be instituted in any court of this state or otherwise.
MCL 205.602