R.I. Gen. Laws § 28-9-7: Selection of arbitrators.

If in the contract for arbitration or in the submission, provision is made for a method of naming or appointing an arbitrator or arbitrators or an umpire, that method shall be followed, but if no method is provided in the contract, the parties to the contract or submission shall agree to the method of naming or appointing an arbitrator or arbitrators or an umpire. If the parties fail to agree, then the director of labor and training, upon application of either of the parties after due notice to the other party, shall appoint an arbitrator to hear the dispute.