Conn. Gen. Stat. § 52-146b

A clergyman, priest, minister, rabbi or practitioner of any religious denomination accredited by the religious body to which he belongs who is settled in the work of the ministry shall not disclose confidential communications made to him in his professional capacity in any civil or criminal case or proceedings preliminary thereto, or in any legislative or administrative proceeding, unless the person making the confidential communication waives such privilege herein provided.