For homes under LA County's jurisdiction, LA County Public Works issues building permits, and its list names additions, alterations, repairs, replacements and system upgrades, not insulation by name, so it isn't settled whether a foam job on its own needs one. The county runs an East Los Angeles Building and Safety office for unincorporated county areas and the cities that contract with it, but some cities nearby run their own building departments, so your address decides where you'd apply. We check which office covers your address before anything else, and when a job calls for a permit, we take care of that step with them before work starts.
We're based in East Los Angeles and work across the cities around it, including Montebello and Monterey Park, plus other nearby cities. A lot of the houses we see are older, with low roofs, cramped attics and garage rooms that bake in summer, which is where closed-cell's thin layer earns its cost. Houses here also sit close together, and national building guidance says attics sealed with no roof vents are much more fire safe where neighbors are close, since embers get into vented attics through the vents.