R.I. Gen. Laws § 28-9.2-8
Within five (5) days from the expiration of the thirty (30) day period referred to in § 28-9.2-7, the bargaining agent and the corporate authorities shall each select and name one arbitrator and shall immediately thereafter notify each other in writing of the name and address of the person so selected. The two (2) arbitrators so selected and named shall, within ten (10) days from and after the expiration of the five (5) day period mentioned in this section, agree upon and select and name a third arbitrator. If, on the expiration of the period allowed, the arbitrators are unable to agree upon the selection of a third arbitrator, the third arbitrator shall be selected in accordance with the rules and procedures of the American Arbitration Association. The third arbitrator, whether selected as a result of agreement between the two (2) arbitrators previously selected or selected by the American Arbitration Association, shall act as chairperson of the arbitration board.
R.I. Gen. Laws § 28-9.2-8