Having grown up there, I always liked Connecticutian as a serious one, but also accepted is Nutmegger (it's the nutmeg state) and best jokey name is Connecticunt (pairs well with our neighboring Massholes)
Yeah but. I lived in Indiana for a long time and most people just say Indianan. Hoosier is more of a Midwest thing. I'm from Arkansas, and that and Florida is a little odd. It's pronounced differently than the state is.
Most people from where? Everyone in Indiana says Hoosier. Maybe it is a Midwest thing, but I don't know how I'd react if someone called me an Indianan. It doesn't even sound correct (admittedly, at least 20% of these sound really awkward).
English is horrible at Demonyms specifically because we've stolen so many words from other languages. It's why the default is actually the phrase, "I am from..." Instead of "I am a/an..."
I had an American history teacher in high school who was adamant we weren't Arkansan because fuck Kansas (paraphrased). He said we were Arkansonian. It doesn't seem to have caught on.