If our customer cashed a $200 check drawn on another bank and this $200 check gets returned to our bank for insufficient funds, is our bank required to provide a customer notice when we first learn of the returned check even though our bank will attempt to clear the check a second time?

Yes, but below $2500, your responsibility to provide notice of dishonor comes from the UCC, not Reg CC. Automatic representment of return items without customer consent is a dangerous practice.

Thanks for clarifying this for me. I'll research the UCC for more information.

Regulation CC wouldn't apply to the check you've described because it was cashed and not deposited. If it had been deposited, however, Regulation CC's http://www.bankersonline.com/regs/229/229-33.html §229.33(d) would require that you provide a notice of the return regardless of the amount (or of the notice, if received under §229.33(a)) by midnight of the banking day following the banking day on which you received the returned check (or notice). That requirement is satisfied by complying with the UCC's notice requirement.

If you fail to timely provide the notice required by Regulation CC or the UCC, and your customer ends up losing money because your delay, you could be responsible for losses sustained by your customer attributable to the delay (UCC 4-214).

When the check is cashed rather than deposited, your right to charge the item back to your customer's account may depend on state law outside the UCC and/or the terms of the customer's deposit agreement with you.