If indeed it is a concrete-encased room with a vault door rather than a freestanding safe, yes, a permit is requires per AJ301.5 of the New York State Residential Building Code (
pg 854):
Level 2 alterations include the reconfiguration of space, the addition or elimination of any door or window, the reconfiguration or extension of any system, or the installation of any additional equipment. Level 2 alterations shall comply with the provisions of Section AJ501 for Level 1 alterations as well as the provisions of Section AJ601 [NOTE: Section AJ601 requires obtaining a permit].
I found no record of RH obtaining permits for any work done in the basement, so I'm pretty sure it was done off-the-books. I did find a sketch of the property on the
Nassau County Land Records Viewer which shows the dimensions of the house:
View attachment 436779
View attachment 436780
I am also attaching a copy of the Property Card from 1/12/2006 which includes detailed information about the house such as materials and structural elements