Can I specify a list of people who can access my safe deposit box if I die?
That depends on state law. Safe deposit laws and rules vary widely from state to state. Iowa law allows a safe deposit box lessor (the bank in many cases) to accept from a box lessee (the customer) a written designation of who may access the box after the customer's death. The Iowa statute was presumably passed in order to allow for a trusted individual to get into the box to remove a will so that it can be submitted to the probate court. There could be other reasons for the law, but that one makes sense.
If you rent the box with someone else, most state laws will allow the surviving lessee to access the box after your death (some states may have some procedural requirements that have to be met in those cases).
Some states don't have a lot of detail in their safe deposit laws, and rely instead on the lease contract to cover access rights. Probably your best source of information for this subject is the institution from which you rent the box. This is certainly a situation that they have to deal with regularly.
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