R.I. Gen. Laws § 17-15-33
If there is a failure to make a nomination or to elect a candidate to party office at any primary by reason of a tie vote, the vacancy, if in respect to an office to be filled by the voters of more than one city or town, shall be filled by the executive committee of the state committee of the respective party, except in the case of a senatorial or representative committee the vacancy shall be filled by the members of the senatorial or representative district committee, as the case may be, and if in respect to an office other than a senatorial or representative district committee to be filled by the voters of no more than one city or town, or a portion of a city or town, the vacancy shall be filled by the city or town committee of the respective political party. The vacancy shall be filled only by the choice of one of the candidates receiving the tie vote. The name of the candidate chosen by the appropriate party committee shall be officially certified to the state board or local board, as the case may be.
R.I. Gen. Laws § 17-15-33