Welcome to the Forum!
I'm chatting big stuff here.
Depends, if it is a registered flag ship of the USA the USCG has the final say.
USCG Small boats stateside the USCG!
USA naval vessels is
NAVSEA
The country of registration has the final say, unless these owners will sometimes default to the American Bureau of Shipping,
www.EAGLE.ORG.
Now the ABS is a listing service in that they detail what a structure in the water is, things need to be met to meet their individual requirements, which will aid the owners in getting insurance and the
maltese cross showing a ships ocean worthy service.
Now here's the trickie part not all requirements of both are the same in any or all respects, can I say life safety is one of these aspects!
It's been a while but you will find out (I doult if it's changed) if you submit, you'll submit to both the ABS and the USCG, again if it is required.
Both can easily require Curves of Form, revised C of F (how the boat will act in the water) or additional calc's when additional equipement is subtracted/added or altered-changed.