Only the property owner, the owner's realtor, the owner's attorney, or the owner's power of attorney can apply for and schedule the certificate of occupancy inspection. Certificate of Occupancy is not required to close; only to occupy the house. This includes moving in personal effects. If the certificate of occupancy is not obtained prior to the closing, then the new owner can apply and schedule after the closing and before moving in.
The buyer can hire a private company to perform a housing inspection prior to taking ownership. However, this is separate from the certificate of occupancy inspection for approval to occupy the dwelling, including moving in personal effects.