California licenses contractors through the Contractors State License Board, and the classification written for pavement markings is C-32, Parking and Highway Improvement Contractor. Its regulatory scope covers applying and installing protective coatings, vehicle stops, guard rails and mechanical devices, directional lines, buttons, markers, signs, and arrows on the horizontal surface of a parking facility, game court, airport, highway, or roadway built of concrete, asphalt, or similar material.
Two details in that scope matter when you are reading a bid. It includes the surface preparation needed to apply those coatings, so cleaning and prep for striping falls inside the classification. It expressly does not include re-paving those surfaces, which is why a company that both paves and stripes typically holds more than one classification, commonly C-12 Earthwork and Paving alongside C-32.
What classification a specific job requires depends on the scope of that job, so treat the above as orientation rather than a rule you can apply to every project. Verify any license number and its classifications through the CSLB's own license lookup before hiring. California also generally requires a license once a project exceeds a small dollar threshold, which most commercial striping work will clear. Classification scope is set in the California Code of Regulations, Title 16, section 832.32.