R.I. Gen. Laws § 17-4-7: New election in absence of plurality.

In case no person receives a plurality of the votes cast in the state or in either congressional district at any election, a new election shall be held in the state or in the district on the fourth (4th) Tuesday after the holding of the election at which there was no choice. For the election, any new certificates of nomination or nomination papers shall be filed ten (10) days previous to the date of the election.