Me. Rev. Stat. tit. 36, § 3914

When the assessor claims that a decedent was domiciled in this State at the time of the decedent's death and the taxing authorities of another state or states make a like claim on behalf of their state or states, the assessor may with the approval of the Attorney General make a written agreement with the other taxing authorities and with the personal representative to submit the controversy to the decision of a board consisting of one or any uneven number of arbitrators. The personal representative may make the agreement. The parties to the agreement shall select the arbitrator or arbitrators.