R.I. Gen. Laws § 17-14-15

A person nominated as a candidate to be voted for at a primary or an independent candidate may withdraw his or her name from the nomination prior to the date of primary by a request signed and duly acknowledged by him or her setting forth the reason for the withdrawal, that the withdrawal is the candidate’s own free act and deed, and that it is not executed as the result of any threat or promise made to the candidate. The certificate of withdrawal shall be filed in the office where the nomination papers were filed within the time prescribed by § 17-14-13 for filing objections to nomination papers; provided, that if an objection has been filed, the certificate need not be filed until twenty-four (24) hours following the decision of the state board, or of the local board, relative to the objection.