Do you store your bank statement in a safe deposit box?

You can, but usually you store things like extra jewelry, deeds, and other things that you want to protect. However, bank statements can easily be shredded, masked, or otherwise disposed of in ways that do not compromise information. If you want to get rid of a statement, you can either make an electronic copy beforehand or just shred it and switch to online electronic statements. It's harder to do this with other paperwork like deeds and full account number lists, and even harder with jewelry and other non-paper valuables.

Simple answer: you can store bank statements in a safety deposit box. It's not quite the best use of the box, but you can put whatever you want in it as long as you have physical room...