R.I. Gen. Laws § 28-9.7-8

Within five (5) days from the expiration of the thirty-day (30) period referred to in § 28-9.7-7, unless the parties mutually agree to extend the time to select their arbitrator, the bargaining agent and the state 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-day (5) period above, agree upon and select and name a third arbitrator. If, on the expiration of the period allowed therefor, the arbitrators are unable to agree upon the selection of a third arbitrator, the chief justice of the Rhode Island supreme court shall select a resident of Rhode Island or a person whose place of business or principal place of employment is in Rhode Island as the third arbitrator upon request in writing from either the bargaining agent or the state authorities. The third arbitrator, whether selected as a result of agreement between the two (2) arbitrators previously selected or selected by the chief justice, shall act as chair of the arbitration board.