Conn. Gen. Stat. § 9-709

(b) If a candidate for nomination or election to the office of Lieutenant Governor is campaigning jointly with a candidate for nomination or election to the office of Governor, the candidate committee and any exploratory committee for the candidate for the office of Lieutenant Governor shall be dissolved as of the applicable date set forth in subsection (a) of this section. Not later than fifteen days after said date, the treasurer of the candidate committee formed to aid or promote the success of said candidate for nomination or election to the office of Lieutenant Governor shall file a statement with the proper authority under section 9-603 , identifying all contributions received or expenditures made by the committee since the previous statement and the balance on hand or deficit, as the case may be. Not later than thirty days after the applicable date set forth in subsection (a) of this section, (1) the treasurer of a qualified candidate committee formed to aid or promote the success of said candidate for nomination or election to the office of Lieutenant Governor shall distribute any surplus to the fund, and (2) the treasurer of a nonqualified candidate committee formed to aid or promote the success of said candidate for nomination or election to the office of Lieutenant Governor shall distribute such surplus in accordance with the provisions of subsection (e) of section 9-608 .

There is no evidence that Subsec. (a) was designed to encourage or discourage nonendorsed candidates for Lieutenant Governor from choosing a particular running mate, rather, the clear purpose is to limit expenditures of candidates for Lieutenant Governor and Governor who are running on the same ticket to amount that the candidate for office of Governor is authorized to spend under election program; campaign expenditures by one candidate in the campaign for general election effectively benefit both candidates; phrase “[a]ny other candidate for nomination or election to the office of Lieutenant Governor” means any candidate for Lieutenant Governor other than an endorsed candidate who is running jointly with the endorsed candidate for Governor, including a nonendorsed candidate for Lieutenant Governor who is running jointly with a candidate for Governor, endorsed or not, and an endorsed candidate for Lieutenant Governor who is running jointly with a nonendorsed candidate for Governor. 297 C. 764.