Castro Valley is unincorporated, so building permits here come from Alameda County rather than a city hall. I won't guess at whether your leveling job needs one. I'll tell you at the estimate, and if it does, we'll file it with the county office for your address or walk you through filing it yourself, whichever you prefer.
When the county requires a permit to alter or repair a structure, the applicant signs a statement that they're licensed under the state's contractor licensing law or explains why they're exempt. California also requires a home improvement contract to carry set information, notices and disclosures that protect you, and any change to it has to be in writing, easy to understand and tell you about your right to cancel.
We're based in Castro Valley and do the same work in Hayward, San Leandro, Oakland, Dublin, Pleasanton and many other cities around it. On older floors here we often find a dip beside an old patch or a ridge where two pours meet, and those are usually the spots that decide how much leveling a room needs.