When more than one claimant applies for the payment of any reward, offered by any county legislative authority, board of commissioners of a port district, or city or town governing body, the county legislative authority, board of commissioners of a port district, or city or town governing body shall determine to whom the same shall be paid, and if to more than one person, in what proportion to each; and their determination shall be final and conclusive.
RCW 10.85.040