You are required to withhold and remit unless the customer tells you not to by signing a properly completed W4-P or its equivalent. Your bank is liable for the amount it should have withheld but did not, regardless of whether you still have the funds on deposit.
Requiring customers to file a written election against withholding sounds a bit lazy...
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.