Interesting question. I think your world's government (governments) would have to be a part of the Federation, at least in some fashion, for someone to be considered a Federation citizen. I can't remember Dax even once referring to herself as a Federation citizen. There might even be a degree of doubt whether Worf ("legally") is a Federation citizen, probably is because of his adoption.
We've seen a Klingon as a senior officer on the Enterprise (Kurn), but that was a exchange program and he didn't wear the Starfleet uniform.