Not a legal expert, so consider this an educated guess.
Place of birth carries some importance when determining Croatian citizenship, but citizenship of parents is much more important and birth in Croatia does not in itself confer Croatian citizenship.
Until the early 1990s Yugoslavia consisted of six republics, of which Croatia was one. Every Yugoslav ...
TL;DR: A Social Security number is not necessary if you are applying for the CRBA and US Passport at the same time
It looks like I need to provide a signed statement. I found this on the US Department of State website:
Do I have to provide by Social Security number on my passport application?
Yes. 22 U.S.C. 2714a and 22 C.F.R 51.60(...