Conn. Gen. Stat. § 1-23: When affirmation may be used.

When any person, required to take an oath, from scruples of conscience declines to take it in the usual form or when the court is satisfied that any person called as a witness does not believe in the existence of a Supreme Being, a solemn affirmation may be administered to him in the form of the oath prescribed, except that instead of the word “swear” the words “solemnly and sincerely affirm and declare” shall be used and instead of the words “so help you God” the words “upon the pains and penalties of perjury or false statement” shall be used.