Safe deposit box regulations and procedures in the event of death of the boxholder can vary depending on specific state laws. The best thing to do is speak directly to the bank manager where the box is leased. In general having someone else authorized to access the box will probably avoid most problems but in some cases there are requirements that the contents have to be inventoried in the presence of a bank officer. This inventory can possibly become involved in claims against, or settlement of, the estate of the deceased, and it is also possible that the contents can be considered as a gift if kept by the person removing them. This can also raise tax liability issues. Again, the best thing to do is speak directly to your bank manager and follow up on any tax issues, etc with the appropriate people knowledgeable about these laws in your area.
One other note on this is that Schedule F of IRS Form 706 (Estate Tax Return) requires reporting if the deceased held a SBD or had access to one, and also requires reporting of collectables held in excess of certain dollar amounts. This form and the instructions are available online at the IRS website. Again, maybe a good subject to discuss with an attorney knowledgeable in estate issues.