Moving out of Louisiana is easy. Stopping Louisiana taxes is a different act, and it happens on paper: Louisiana keeps treating you as a resident until the record shows otherwise.
On the burden of showing otherwise: The department asks for documentation confirming domicile in the other state — the other state's voter registration, automobile registration, and driver's license among them — so the record is supplied by the person claiming the change.
Two tests decide it. Cross 183 days with a Louisiana abode still available and you are taxed as a resident regardless of where you claim to live — and see day-counting rules. Or keep the day count clean but leave the life-pattern evidence pointing at Louisiana, and domicile does the same work. Everything on this page exists to answer one question: if LDR asks, does your record hold?