Castro Valley is unincorporated, so building permits here come from Alameda County rather than a city office, and you apply through the county's online permit portal. If your basement project needs a permit, I'll say so at the estimate and take care of filing it with the county, or walk you through it if you'd rather file it yourself.
In California, flooring work falls under its own license class with the state licensing board, covering every kind of floor except ceramic tile. Small jobs count too. Work under $1,000 still needs a licensed contractor whenever it needs any permit or the person doing it brings on helpers, so a low bid from someone unlicensed isn't the shortcut it looks like.
We're based in Castro Valley and do the same basement work in Hayward, San Leandro, Oakland, Dublin, Pleasanton and many other cities around it. The basement calls we get tend to sound alike. There's an older slab, an old floor coming up, damp patches near the walls, and a homeowner who wants to finish the space without repeating the problem.