R.I. Gen. Laws § 29-4-5
Whenever any city or town shall establish a free public library, or shall become possessed, as provided in this chapter, of any free public library, the city council or town council, as the case may be, shall proceed to elect a board of trustees, to consist of not less than three (3) members nor more than seven (7). As soon as possible after the election of the first board, the members thereof shall meet and be divided by lot into three (3) groups or classes, the terms of office of one group expiring in one year from the date of their election, those of another group in two (2) years, and those of the remaining group in three (3) years. With the expiration of the term of office of any member, the vacancy shall be filled by the city council or town council, as the case may be, for the term of three (3) years. Vacancies occurring by resignation, removal, death, or otherwise, shall be filled as above for the unexpired term thereof.
R.I. Gen. Laws § 29-4-5