I believe the answer is no.
This is an agreement between the bank and the customer, and we generally don't require witnesses for other types of agreements (like signature cards or loans). The last document I remember that required a witness - apart from wills & certain trust documents - was the mortgage, and that requirement went away a few years ago.
The only thing I can tell you with certainty is, my banks don't require it.
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Opinions are Bartman's, not those of my employer. "A noble spirit embiggens the smallest man."