Conn. Gen. Stat. § 9-453c: When single petition may be used.

The names of any or all candidates under the same party designation for state offices, as defined by section 9-372, and for the office of presidential elector may be included in one nominating petition, but the name of no candidate for any other office shall be included therein, provided the names of any or all candidates under the same party designation for at-large municipal offices to be filled at a municipal election may be included in one nominating petition.