Castro Valley is unincorporated, so Alameda County handles building permits here, and owners apply through the county permit portal. Whether a polishing job needs a permit isn't something I'll guess at. If yours does, I'll say so at the estimate, and we'll file it with the county for you, or walk you through it if you'd rather file it yourself.
Grinding concrete makes fine dust. California's worker safety rules require a dust reduction system whenever powered tools grind concrete, unless air sampling on that job shows exposure stays within set limits. The same rule names silicosis, lung cancer, chronic obstructive lung disease and reduced lung function as risks of breathing too much of it, so we treat dust control as part of the grinding itself.
We're based in Castro Valley, and we also work in Hayward, San Leandro, Oakland, Dublin, Pleasanton and many other cities around it. Polished concrete can look different from one area to another, because the type, size and spread of the stone in the mix varies. That's one more reason the sample on your own floor matters.