R.I. Gen. Laws § 45-4-9: Failure by electors to elect officer.

If any town, on the day of any election for town officers, fails to elect any of the officers whom they may lawfully choose, except town clerk, town council, and town treasurer, the officers shall be elected by the town council of the town at its next meeting; provided, that town councils may postpone the election of any of the officers to some future meeting. The several towns have full power to delegate to their respective town councils the election of any of the officers whom the town may lawfully choose, except town clerk, town council, and town treasurer.