In my home state, failure to find an asset in the name of the garnishee makes the bank liable for the entire amount of the judgment, not just the funds it had on deposit. For example, the garnishor has a $25,000 judgment and serves a garnishment on your bank, but you only held $500 in the name of the garnishee. If you mistakenly return that garnishment "no assets found" your bank owes $25,000.
That provides a more than adequate incentive for conducting a diligent search, including a manual search. As for being able to defend your bank's failure to locate an asset by pointing out an acknowledged weakness in your system, I do not like your chances.
In C Notice processing the IRS imposes a standard that translates to: Look as hard as you would if you were processing a claim on behalf of your bank. So in training sessions I use the anecdote: The CEO stops by your office and says, "I am going to have to charge off a loan, see if this borrower is on any accounts where we can claim a right of offset." Would your bank really just do a numeric search and then drop it? Whatever you would do if the CEO asked you to find an account is what you should do in response to a demand from a third party.
Check to see what the penalty is in your state. FYI, failure to turn over assets rightfully seized by the IRS generates a penalty equal to the amount of assets you held plus 50%, regardless of whether you still hold those assets. In the above example, you would owe the IRS $750 even if the customer had closed his account.
Do your homework on the penalties under state law. Then, start talking about the risks involved and doing manual searches vs. updating your record keeping system and the ancillary benefits that effort might offer. When you are talking about both options, the second is going to sound a lot more desirable than the first.
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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.