If the taxpayer uses an IRS approved self-select PIN for e-file, the DRS will accept this PIN as the State signature. By adopting this PIN alternative, the DRS has effectively removed the need for the Form CT-8453.
No documents need to be mailed to the state if the return is accepted through e-file. Only if you are mailing a "payment" with the payment voucher would you need to send information to the state.