I have to disagree with @Medicinefuture, respectfully. Most belief systems regard demonic possession as a psychical and physical process, as they believe that the demon is trying to force the will of a person into submission so that the demon can be the dominant will in the body, thus take over it.
Possession is technically in the DSM, the official diagnostic criteria reference of the American Psychiatric Association. It does not state "demonic possession" however. In the “DSM-IV-TR™", Under the code # 300.15 - Dissociative Disorders Not Other Specified, paragraph 4, it is stated:
“4. Dissociative trance disorder: single or episodic disturbance in the state of consciousness, identity, or memory that are indigenous to particular location and cultures. Dissociative trance involves narrowing of awareness of immediate surroundings or stereotyped behaviors or movements that are experienced as being beyond one’s control. Possession trance involves replacement of the customary sense of personal identity by a new identity, attributed to the influence of a spirit, power, deity, or another person, and associated with stereotyped “involuntary” movements or amnesia and is perhaps the most common Dissociative Disorder in Asia. Examples include amok (Indonesia), bebainan (Indonesia), latah (Malaysia), pibloktoq (Arctic), ataque de nervos (Latin America), and possession (India). The dissociative or trance disorder is not a normal part of a broadly accepted collective cultural or religious practice.”
Demonic possession is often documented when an exorcism occurs. The Catholic Church requires exorcisms to be documented, but I am not sure of other denominations or religions. If it can be "properly documented" is really a matter of opinion, what you mean by "properly documented" as well.