There are no definitive signature requirements under TILA, so considering the new TRID rules, the Loan Estimate nor the Closing Disclosure require a signature. A signature can be included at the option of the creditor according to the regulation 1026.37(n) and 1026.38(r).
Other disclosures that will require a signature are the Flood Notice, insurance acknowledgement if credit insurance is offered.
Many times, the financial institution will establish policy/procedures that require signature. In addition, state law should be reviewed as well to insure a signature is not required.