R.I. Gen. Laws § 17-11-10: Filling of vacancies by town council.

In case of the death, resignation, or permanent disability of the moderator of any town, or of the moderator or clerk of any senatorial or representative district, except in the cities of Providence, Pawtucket, Central Falls, Warwick, Cranston, Woonsocket, and Newport, or of any voting district in any town, except the towns of Barrington, Middletown, and Warren, not divided into senatorial or representative districts, the town council may fill the vacancy from the list of registered voters submitted by the party chairperson under whose party designation the moderator or clerk had been elected. In the absence of a submitted list, or, if the person, when elected, was not affiliated with any party, the town council may make its choice from the list of registered voters.