When a register claims that a decedent was domiciled in this State at the time of death and the taxing authority of another state makes a similar claim on behalf of that state, then, with the approval of the Attorney General of this State, the Comptroller may make a written agreement with the other taxing authority and with the personal representative to submit the controversy to the decision of a board consisting of 1 or any other uneven number of arbitrators. The personal representative may make the agreement. The parties to the agreement shall select the arbitrator or arbitrators.