Conn. Gen. Stat. § 9-465: Placement of candidate names on ballot.

The name of a candidate shall be placed on the ballot at a primary of a party either: (a) By direction of the secretary when he determines, within the time specified in section 9-466, that the candidacy of such person for such party's nomination for President is generally and seriously advocated or recognized according to reports in the national or state news media, unless such candidate files a request as provided in section 9-466; or (b) by petition to the secretary as provided in sections 9-467, 9-468 and 9-469.