I know under REg CC my bank can hold a check that I deposit. Can it also hold a check taht I cashed under Reg CC or is that just their bank policy?

Typically a bank will place a hold on existing funds in the account equal to the amount of the check cashed, unless the check that was cashed was drawn on the same bank.

Regulation CC will permit a bank to place a hold on other funds of the depositor as if the check being cashed were deposited.

So holds on checks cashed are covered by Reg CC?

If the holds are placed on a customer's transaction account. State law may expand the coverage to savings and MMDA accounts, too.

I hasten to add that this doesn't include holds placed on the account on which the check is drawn. That's simply a matter of grabbing the balance to cash the check. Regulation CC will cover a hold placed on a transaction account for the purpose of cashing a check drawn on another account.