I have a class C misdemeanor in CT, and I live in AZ. Statute of limitations?

The statute is the time between committing the crime and being charged. You were charged so the statute doesn't apply. The warrant will only go away if you get arrested, turn yourself in or die. I'm no expert on interstate fugitive apprehension, but it's safe to say there's a chance they'll knock on your door or arrest you at a traffic stop. You can't take care of it over the phone.