No, but they do want you to let them know if you don't "owe any money to the taxpayer." Your incentive for doing that is to get them to leave you alone in the future.
I never really thought about it before, but there isn't a lot the IRS could do about it if a bank failed to forward the copy of the Notice of Levy even if there were funds subject to the claim.
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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.