R.I. Gen. Laws § 17-2-3
When both the governor and lieutenant governor elect, or one among the lieutenant governor, secretary of state, attorney general, or general treasurer elect, are incapacitated, or when there has been a failure to elect one or more of the officers mentioned in this section, the general assembly shall, upon its organization, meet in grand committee and elect some person or persons to fill the office or offices, as the case may be, for which the incapacity exists or as to which the failure to elect occurred. When the general assembly elects any of the officers because of the failure of any person to receive a plurality of the votes cast, the election in each case shall be made from the persons who received the same and largest number of votes.
R.I. Gen. Laws § 17-2-3