If only this state and one other state are involved, the Department and the taxing official of the other state shall each appoint a member of a board of arbitration, and these members shall appoint the third member of the board. If this state and more than one other state are involved, the taxing officials thereof shall agree upon the authorities charged with the duty of administering the laws relating to death taxes in three states not involved in the dispute and each of these authorities shall appoint a member of the board of arbitration. The board shall select one of its members as chair.