Safety deposit box

yes.They have to know all the contents of your safety deposit box for the insurance.They need to know the value so they'll know how much to pay you if in case the box got lost or the bank has been robbed.

I don't think so. It should be private and they should not know what it is. But it asl depends, when you say safety deposit box you can also have it at home which is what I am referring to on my first sentence. The other one is that safety deposit box can which are taken cared of by the banks are checked before being accepted for safekeeping therefore they should know what's inside for their secirity as well and assessment of the value.