Some states also had the word bas*ard on them if parents were not married- I have seen that on old BCs, where it asked for father’s name- don’t know when they quit doing that. Maybe long before 1961- but I don’t know- I saw it on certificates from the 1940s.
Obama says in his autobiography that he never took the time to nail down whether his parents were actually married. Given his penchant for shading the truth, I suspect what that really means is that he found out they were never married but does not want to admit it.
It makes no sense to me that an attorney obsessed with his background would have made no such effort, especially given how simple it would have been while he was working at a law firm.
Obviously the only way to know for sure is to visit the HI courthouse and search the records for evidence of the Obama divorce. If it's not there, they were never married.