When a FI rents a safe deposit box to itself is a leasing agreement still needed? Or is only a Corporate Resolution only needed? Or both?

Most banks I have worked at complete a lease agreement. With the responsible party for the box signing the lease agreement. They will then attach a list of those authorized to enter the box to the lease agreement. I have never known a bank to use a corporate resoluation in renting a box.

What you need is controls over access and a way to ensure the box is removed from inventory so that it can't be mistakenly rented. The contract is probably superfluous, but if it becomes the frame on which the access list is placed, there's certainly no harm.

I recommend using positions as opposed to specific names since they can change quite often.

For example, it may state something like: two bank employees required to enter box; at least one must be an officer.