In Chico, the Building Division issues permits, and city code requires one to alter, improve, repair or remodel any building or its service equipment. Whether your sealing job falls under that depends on what it includes, so I don't assume either way. If it needs one, we handle the application and inspection. Work that changes duct work, heating or venting comes under the city's mechanical permit.
Contractors who pull a Chico permit need a current city business license and a current California contractor's license, and the state's insulation classification covers installing insulating material, which matters when a sealing job adds insulation. On jobs around Chico and out in Durham and Oroville, we see plenty of older houses with gas water heaters, can lights and attic hatches nobody ever sealed.