Beth, our bank has a Safety Deposit Box Operation Manual. Our state does not require an inventory to be taken of the box, under a succession. The succession is required to close a box, however, we have found that it is wise to continue doing so.
However,if the renter dies, and I am assuming that there are no survivors, it would seem prudent to get court orders.
Our policy states that 2 bank representative employees (one of which is a bank officer) must be present during the box entry and only the items that the court order specifies can be removed from the box.
Of course, there are different requirements and or stipulations regarding who can enter the baox when they are jointly held, Partnership boxes, corporate boxes, business boxes (such as churches or civic clubs) etc.
I'm not sure if this helps, but this is our method. I think that just because your state no longer requires inventory, it does not mean that you can't perform it.
Hope someone else out there can give you more insight.