Conn. Gen. Stat. §36a-42 states that a financial institution may not disclose any financial records relating to a customer unless the customer or his agent authorizes disclosure or unless it is in response to certain legal procedures (i.e. a subpoena or court order). See also Conn. Gen. Stat. §36a-44 (exceptions re: confidential treatment of customer records).
There are no reported court decisions on the issue of whether a bank is a "public agency" within the meaning of Conn. Gen. Stat. §1-200(1). See Records Outline at II.A.2.h and j (certain financial records held by a public agency are exempt from disclosure).