There is not a requirement that it be signed. That being said, getting it signed or some how documenting when and how it was delivered is a great idea and one I would highly encourage. That is just proof to auditors and examiners that you did indeed meet any kind of timing requirement.
That can be done through the customer signing, documentation by the loan officer, or if mailed a cover letter listing all of the documents that were mailed. This is not an all inclusive list but are some great ways to document.