Conn. Gen. Stat. § 9-453r

(b) On the horizontal rows below the rows so used for candidates, if any, who are so entitled to a party designation on the ballot, shall be placed, in the appropriate office columns, the names of candidates contained in petitions approved pursuant to section 9-453o bearing no party designation. Such candidates shall not be entitled to separate rows. Precedence as to horizontal row between or among such candidates shall be determined, if necessary, by the order in which their applications for petitions were filed with the Secretary of the State from the earliest to the latest; provided that within any such horizontal row the names of as many of such candidates for the same multiple-opening office as such row will accommodate shall be placed before placing the names of other such candidates for such office on the next such row. The order of the names of such candidates for the same multiple-opening office, within and between any such horizontal rows, shall be determined by the registrars of voters by lot in a ceremony which shall be open to the public. The registrars of voters shall provide at least five days public notice for each such ceremony. Each row in which a candidate's name appears who is not entitled to a party designation shall be labeled “Petitioning Candidates”, the print of which shall correspond to that used for party designations.

See Sec. 9-249b re arrangement of ballot when number of party designations and petitioning candidate rows on ballot exceeds nine.