La. Rev. Stat. § 29:764

Authority. The state health officer has exclusive authority to isolate or quarantine to prevent the spread of contagious disease. If a parish becomes infected with a disease to the degree that it threatens to spread to another parish, the state health officer can quarantine that parish. Parish health officers may establish quarantine only with permission of the state health officer and parish legislative body, and shall be supervised by the state health officer.

La. Rev. Stat. Ann. § 40:6

Penalties. Whoever violates those provisions of the sanitary code dealing with the isolation or quarantine of communicable disease, or any person having such a communicable disease that may cause a severe health hazard to the community and who, after having been officially isolated or quarantined by any local health officer or by the state health officer or the duly authorized representative of either health officer, violates the provisions of the isolation or quarantine shall be fined not less than $50 nor more than $100or be imprisoned for not more than two years, or both.