Current examination procedures suggest that "customer due diligence" at account inception would have put the bank in a better position to evaluate the cash deposits. In short, you're going to need the information anyway, you might as well ask them about the focus of their practice, the types of items they will be depositing, etc. when the account is opened. Now, they are more likely to be resistive.
When you go visit them to have this conversation, see if you see enough traffic in their office to account for $35,000 in cash in three days when all the debtors are paying is phone bills. In addition, look at their deposits to see if they include other items; e.g. PMOs, official checks etc. which most people would use to pay a past due bill. I'm not buying this explanation, but note that they may have one I would buy.
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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.