R.I. Gen. Laws § 17-3-3
If it appears by the count of the state board that no election has been made of any one or more of the senators or representatives in the general assembly, at any election held for those officers, the board shall, immediately after the count, notify the secretary of state of the failure to elect; the secretary of state shall, immediately after the notification, direct the local boards in the senatorial or representative districts to issue their warrants to the moderators of the district, districts, or voting districts, as the case may be, directing the election to proceed on the tenth (10th) day from the date of the warrant, unless the day is a legal holiday, in which case the secretary of state shall direct the election to proceed on the next day after the tenth (10th) day not a legal holiday, for the officer or officers for which there was no choice, which warrant shall be served on the day of its issue by the several city or town sergeants or constables; provided, there shall be no election held on Saturday, and if the tenth (10th) day falls on Saturday, the election shall proceed on the Monday next following, unless that Monday is a legal or religious holiday, in which case the election shall proceed on the next following day which is not a legal or religious holiday.
R.I. Gen. Laws § 17-3-3