Conn. Gen. Stat. § 12-39aa

(2) If the postmark is illegible, omitted or purported to be erroneous, the person who is required to file the return, claim, statement, or other document, or to make the payment, shall bear the burden of proving by competent evidence that such return, claim, statement, or other document or payment was deposited in the mail in the United States on or before the due date for filing, or payment.

(3) If the return, claim, statement or other document or payment, is sent by United States registered mail, it shall be deemed to have a postmark date that is the date of registration, and, if sent by United States certified mail, it shall be deemed to have a postmark date that is the date that the sender's receipt is postmarked by the postal employee.

(b) Unless it is otherwise determined by the commissioner to be inadequate for the needs of the state, (1) any reference in subsection (a) of this section to the United States mail shall be treated as including a reference to any delivery service designated by the Secretary of the Treasury of the United States pursuant to Section 7502 of the Internal Revenue Code of 1986, or any subsequent corresponding internal revenue code of the United States, as from time to time amended, (2) any reference in subsection (a) of this section to a postmark made by the United States Postal Service shall be treated as including a reference to any date recorded or marked in the manner described in said Section 7502 of said Internal Revenue Code by a designated delivery service, and (3) any equivalent of registered or certified mail designated by the Secretary of the Treasury of the United States pursuant to said Section 7502 of said Internal Revenue Code shall be included within the meaning of registered or certified mail as used in subsection (a) of this section.