I do not believe you need to give the customer a copy, but you must have a signature from applicant and co-applicant verifying they received the disclosure.
A good example would be a Visa application. Does your bank offer insurance from another company with the Visa application? and did that company require your Visa application be revised with the disclosure? But was there a way to provide the customer with a copy or was the customer's signature sufficient? This example was from our Visa applications, but they also needed updating for Reg Z.
Opinions are mine, not my employer.