In accordance with the provisions of § 51-14, the judges of the Superior Court may make such rules as they deem necessary to provide a procedure in accordance with which the court, in its discretion, may refer to an arbitrator, for proceedings authorized pursuant to this chapter, any civil action in which in the discretion of the court, the reasonable expectation of a judgment is less than fifty thousand dollars exclusive of legal interest and costs and in which a claim for a trial by jury and a certificate of closed pleadings have been filed. An award under this section shall not exceed fifty thousand dollars, exclusive of legal interest and costs. Any party may petition the court to become eligible to participate in the arbitration process as provided in this section.