R.I. Gen. Laws § 17-4-8
Whenever any person elected a representative in congress from either district, at any time between the day of his or her election and the beginning of his or her term of office, refuses to serve and so declares to the secretary of state, or dies, becomes insane, removes from the state, or is otherwise incapacitated, or whenever a vacancy happens in the representation of this state in congress as contemplated in the second section of the first article of the Constitution of the United States, the governor shall immediately issue his or her writ of election directed to the several city and town clerks, or local boards as the case may be, ordering a new election of the representative in congress to be held in that district to fill the vacancy, at as early a date, to be stated in the writ, as will be in compliance with the provisions of law in relation to these elections, but no election provided for by this section shall be held on any day other than the first Tuesday next after the first Monday of any month; provided, that whenever a vacancy occurs between the first day of April and the first day of October in any even-numbered year, the governor shall, unless in his or her opinion the public good requires an earlier special election, issue his or her writ for a special election to fill the vacancy to be held with the general election on the Tuesday next after the first Monday in November of that year.
R.I. Gen. Laws § 17-4-8