If you are accepting the consumers dispute, no written notice is required by Reg E. If you are denying the customer's claim, ยง1005.11(d) requires a written notification:
In addition to following the procedures specified in paragraph (c) of this section, the financial institution shall follow the procedures set forth in this paragraph (d) if it determines that no error occurred or that an error occurred in a manner or amount different from that described by the consumer:
The institution's report of the results of its investigation shall include a written explanation of the institution's findings and shall note the consumer's right to request the documents that the institution relied on in making its determination. Upon request, the institution shall promptly provide copies of the documents.