The town council of any town or the legislative body of any city, except the cities of Providence, Newport, Central Falls, Cranston, and Warwick and the towns of Bristol, Charlestown, Johnston, Narragansett, North Kingstown, South Kingstown, Warren, Westerly, and North Providence may by ordinance provide that whenever a person shall be charged with a violation of a provision of any of its ordinances relating to traffic, the jurisdiction and cognizances of violations of which ordinance is in the district court, and the person is notified in writing by a police officer to appear on a day and hour stated in the notice to answer the charge before a division of the district court having jurisdiction, the person, instead of personally appearing in court, may, in person or by one duly authorized by him or her in writing, appear before the clerk of the division of the district court having jurisdiction, admit the truth of the charge and pay to the clerk any fine that the court may from time to time, by standing order or rule establish or as may be fixed by the ordinance enacted under this section as the fixed penalty for those violations, not to exceed in any case the maximum fine imposed by law; provided, that appearance, admission, and payment is made at the office of the clerk during the office hours of the clerk within seven (7) days of the notification, and failure to appear within that time shall be deemed a waiver of the right to dispose of the charge without personal appearance in court. The payment of the fine to the clerk in the manner provided in this section shall operate as a final disposition of the charge and the proceedings shall not be deemed criminal. The notice shall indicate the offense charged and shall also contain any information that will enable the person charged to take advantage of the provisions of the ordinance enacted under this section.