My bank offers a traditional ODP LOC (overdraft protection line of credit) that can only be drawn on when the linked checking account becomes overdrawn. If the account holder requests that we close the checking account, does the customer also have to expressly state that they want us to close the ODP LOC before we can close the line?

That is all up to your contractual agreements.

welcome with your first post!

you state the LOC can only be drawn on when the linked checking account is OD. if you close the checking account, what reason would you have for leaving the LOC open, if it no longer can be drawn on, since it is no longer linked to an account? this question assumes you don't let them close the account if there is a balance in the LOC or the checking account is not positive.

In fact, it is important that you have a strict procedure for such situations so that you don't knowingly let such a LOC remain open if the customer asks to have the checking account closed (or if the bank decides to close the account). And customers should be aware of your policy, if there can be no ODP LOC without a checking account. And banks with these LOCs should get (and pay attention to) reports when any auto-payment from the checking account to the LOC fails for insufficient funds.