Conn. Gen. Stat. § 2-4
When the Senate and House of Representatives join in convention for the election of any state officer, the roll of each house shall, before any ballot is taken, be called by its clerk, and each member shall rise and answer to his name; and the names of those absent shall be entered on the journal of the house to which they belong. If, on any ballot, the whole number of votes exceeds the number of persons who have answered to their names, the president shall, before declaring the ballot, cause the names of absentees to be called and, if any answer, shall inquire if they have voted; and if the number of votes still exceeds the number of persons who have answered to their names, and if such excess of votes, subtracted from the highest number given for either candidate, is sufficient to change the result, the convention shall order another ballot.
Conn. Gen. Stat. § 2-4
(1949 Rev., S. 3.)