Appendix D of HMDA Reporting Getting It Right on page D-9 states "in reporting the date of application, report the date the app was received or the date shown on the app." It goes on to say you do not have to choose the same approach for the entire submission, it should generally be consistent - such as by routinely using one approach within a particular division of the institution. So, you should be ok as long as each dept. is consistent.
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Opinions are mine and subject to change frequently