Question:

Are appraisers required by USPAP to retain a paper copy of electronically transmitted appraisal reports?

Response:

No. The Record Keeping section of the ETHICS RULE requires appraisers to prepare and retain written records of appraisal, appraisal review, and appraisal consulting assignments. However, the Comment states: 

A photocopy or an electronic copy of the entire actual written appraisal, appraisal review, or appraisal consulting report sent or delivered to a client satisfies the requirement of a true copy.

Therefore, a paper copy is not required.