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 a fact-finder for proceedings authorized pursuant to this chapter, any contract action pending in the Superior Court, except claims under insurance contracts for uninsured and underinsured motorist coverage, in which only money damages are claimed and which is based upon an express or implied promise to pay a definite sum, and in which the amount, legal interest or property in controversy is less than fifty thousand dollars exclusive of interest and costs. Such cases may be referred to a fact-finder only after the certificate of closed pleadings has been filed, no claim for a jury trial has been filed at the time of reference, and the time prescribed in § 52-215 for filing a jury trial claim within thirty days of the return day or within ten days after the issue of fact has been joined has expired.