The phrase you’re looking for is safe-deposit box, not safety-deposit box. The latter is an eggcorn resulting from a mishearing of the former. The mistake is understandable because the first two syllables of safe-deposit box sound like safety.
A little web research shows that safety-deposit box is used about half as often as safe-deposit box, making this a very common error. Safety-deposit box even makes it into some reputable publications—for example:
It’s the online equivalent of a giant safety deposit box. [Los Angeles Times]
She says the detective made her promise to get a safety-deposit box for the medal. [AP]
These writers use safe-deposit box correctly:
Placing an order feels a little like taking your great-grandmother’s jewels from a safe-deposit box. [Village Voice]
The financial record file should provide the location of a safe-deposit box, if applicable, and the name or names of those who have access. [Ventura County Star]
