There is no requirement for a signature to pull credit, if that is what you are getting at:
Sec. 604. Permissible purposes of consumer reports
(a) In general. Subject to subsection (c), any consumer reporting agency may furnish a consumer report under the following circumstances and no other:
(3) To a person which it has reason to believe
(A) intends to use the information in connection with a credit transaction involving the consumer on whom the information is to be furnished and involving the extension of credit to, or review or collection of an account of, the consumer; or
by Richard Insley:
From the safety & soundness point of view, you must always think about credit applications as "Exhibit A." If, at some later date, you find it necessary to sue for collection, you want to have documents that tie the applicant to the representations made to obtain the loan. Maybe the applicant omitted or lied about something. If s/he signed (or e-signed) the lie, then you have a strong case. Without some form of signature(s), you have a p-ing match where the customer claims s/he has no idea where you got the information. Getting the applicant(s) to sign (or e-sign) a copy of the electronic application at closing would get the job done.