Conn. Gen. Stat. § 2-40

(b) Notwithstanding the provisions of section 4-19 , no vacancy in the position of Chief Justice or judge of the Supreme Court, Appellate Court or Superior Court shall be filled by the Governor when the General Assembly is not in session unless, prior to such filling, the Governor submits the name of the proposed vacancy appointee to the committee on the judiciary. Within forty-five days, the committee on the judiciary may, upon the call of either chairman, hold a special meeting for the purpose of approving or disapproving such proposed vacancy appointee by majority vote. The Governor shall not administer the oath of office to such proposed vacancy appointee until the committee has approved such proposed vacancy appointee. If the committee determines that it cannot complete its investigation and act on such proposed vacancy appointee within such forty-five-day period, it may extend such period by an additional fifteen days. The committee shall notify the Governor in writing of any such extension. Failure of the committee to act on such proposed vacancy appointee within such forty-five-day period or any fifteen-day extension period shall be deemed to be an approval.

(c) Prior to a public hearing on a judicial nomination, the judiciary committee may employ a person to investigate, at the request of the cochairpersons of said committee, any judicial nominee with respect to the suitability of such nominee for judicial office. Such investigator shall report his findings to said committee and any such report shall be confidential and shall not be subject to public disclosure. Such person shall receive such compensation as may be fixed by the Joint Committee on Legislative Management for each day he is engaged in his duties as an investigator.

See Sec. 4-2 re referral of judicial nominations to committee on the judiciary.