by Jim Bedsole: You would only need to comply with E-SIGN if you were substituting the paper statements with electronic statements. If you are just supplementing them with electronic, no E-SIGN opt-in is required.
by Richard Insley: You are required to be compliant with Regs. E, DD, and any other regulation of your products.
These product regulations require you to disclose certain aspects of the product or service before and during the time your customer uses each product. Some of these before/during disclosures must be "in writing" (because Regs. E, DD, etc. say so)--including most deposit account (consumer only) statements. As Jim advises, you only need to use ESIGN to satisfy one of these "in writing" rules when you offer and your customer consents to e-delivery as an alternative to paper.