It varies. Call your town for specifics.
In an effort to cut costs, municipalities will share inspectors, making them available only a day or two per week.
But, if you need one quickly, let them know. Some will expedite the process for you for a fee.
It varies by municipality. The best thing to do is to check with the building department or the department in your town that arranges for a certificate of occupancy. Don't forget that you may also have to get a smoke detector and carbon dioxide certificate which may or may not be part of the certificate of occupancy requirement. Additionally, many towns use alternate names for the certificate of occupancy requirement.