R.I. Gen. Laws § 45-4-16: Filling of vacancies in office.

(a) Whenever a vacancy occurs in any office by death, removal out of town, resignation, or by neglect or refusal to qualify, or for any other cause, the town council may fill the office until the next town meeting for the election of officers. Whenever from any cause there are vacancies in the town council of any town, so that there are not sufficient members to form a quorum, the town clerk shall call a special town meeting in the manner provided by law for calling special town meetings, at which meeting, or at any subsequent meeting called for that purpose, vacancies shall be filled in the manner provided for the election of officers.

(b) Whenever a vacancy occurs in the town council of the town of West Warwick, and the town council for any reason fails to fill the vacancy within thirty (30) days after the office becomes vacant, then the town clerk shall call for a special election in the manner provided by law; however, no special election shall be called where the vacancy occurs within nine (9) months of the next general election.