It seems convenient, real-estate-wise, to say that a room must have a closet in order to be considered a bedroom. NOT true. Older homes used to rely on freestanding wardrobes and dressers in bedrooms. So many Victorian homes, for example, don't have closets in rooms used as bedrooms.
But there are specific requirements.
Here's a link you may find interesting. It refers to California building code. http://www.sonoma-county.org/prmd/docs/policies/1-4-1.pdf
Bedroom: any space in the conditioned area of a dwelling unit or accessory structure which is 70 square feet and greater in size and which is located along an exterior wall, but not including the following: hall; bathroom; kitchen; living room (maximum of one per dwelling unit); dining room (in proximity to kitchen, maximum of one per dwelling unit); family room (maximum of one per dwelling unit), laundry room, closet/dressing room opening off of a bedroom.
The Director of PRMD or his/her designee may grant exceptions if a room, by its design, cannot function as a bedroom. Sewing rooms, dens, studios, lofts, game rooms, and any other conditioned room along an exterior wall which is 70 square feet or greater in size will be considered to be bedrooms unless the room is
If a home office, library or similar room is proposed, it may be exempted from being considered a bedroom if there is no closet and at least one of the following is present: a) permanently built-in bookcases, desks and other feature that encumber the room in such a way that it cannot be used as a bedroom; b) a minimum 4 foot opening, without doors, into another room; or c) a half wall (4 foot maximum height) between the room and another room. A detached building which contains only a half bath will not routinely be considered as having a bedroom unless it is specifically identified and permitted as a guest house.
When an exception is made per the above, it shall be documented in Permits Plus in the comments section so that all staff are aware of the determination. A conditional statement may be required to be signed by the property owner if the permit is for an outbuilding which has been determined to be a use other than a bedroom or other living space. This statement may be recorded as necessary to inform future property owners of restrictions on use of the building.