R.I. Gen. Laws § 8-9-11
The probate court of any town or city shall take the probate of wills and grant administration on the estate of deceased persons who, at the time of their decease, were inhabitants of or residents in the town or city, and of other persons, not having any residence in this state, who die leaving rights, credits, or estates, real or personal, within the town or city; provided, that the first probate of the will, and the first grant of administration on the estate, of any deceased person who, at the time of his decease, was not an inhabitant of or resident within this state, shall bar any other probate or grant of administration, although the deceased person may have left rights, credits, or estates, real or personal, in any other town or city in this state.
R.I. Gen. Laws § 8-9-11