R.I. Gen. Laws § 17-15-4: Municipal primaries other than at time of general primaries.

In those cities and towns that now by law hold elections for city or town officers on a day other than the Tuesday after the first Monday in November biennially in each even year, a primary election for the nomination of the city or town officials shall be held and the local board shall fix the date of the election; provided, that the primary election shall have been held by the first Tuesday after the first Monday in the month preceding the date fixed for the election; and provided, further, that the date fixed by the local board shall not be a religious holiday and shall be held on the first Tuesday next after the first Monday of any month.