The City of Bellaire states on their website that either the occupant or the Seller/Landlord must go to the community development center to apply for a certificate of occupancy when an existing home is for sale or rent. I called the City of Bellaire's Development Services department in order to determine if a CO was needed for new construction. The gentleman advised that you receive a CO at the end of the construction process. Only new construction homes and homes being rented out will require a CO. He stated that you do not need one if you are purchasing an existing home (which is contrary to what they have on their website).
Here is the contact info for the Development Services for Bellaire in case you want to reach out personally.
This is from the City of Bellaire FAQ Page: "A Certificate of Occupancy is needed anytime an existing home is either for sale or for rent. The occupant or the seller/landlord must come to the community development office and apply for a certificate of occupancy. Commercial properties also require a Certificate of Occupancy. " http://www.bellairetx.gov/faq.aspx?TID=8