This is tough. In 1991 our 17 year old adopted daughter walked off the top of a 17 story building. She had been in and out of therapy, and was at that time in treatment. After her death her therapist told us that they, at her clinic believed her to have multiple personalities. I asked our bishop at the time if that was demon possession and he never really gave me a clear answer. Do you think you could give me a clear answer to this? Are multiple personalities really demons who mix that person up? This has haunted me for years.
The academic world, including the medical profession, is not equipped to consider theological matters. It is not that the scientists and doctors are not necessarily religious people, but the structure of academic technology cannot detect or measure spiritual phenomena. So doctors and scientists cannot give you an answer to your question.
From the religious point of view, I know of no specific rules by which demonic possession can be measured. However, those who hold the holy priesthood have power through that priesthood over evil spirits. That power is exercised under the direct inspiration of the Holy Spirit. And although not as common as other ministrations of the priesthood, it does exist and is used. In those cases there is no doubt whatsoever that when an evil spirit is commanded to leave a person, and the person immediately comes to himself/herself, and expresses the feelings of possession and the feeling of relief therefrom, that the person was, and is no longer, possessed by an evil spirit. So in any particular case of apparent possession, where the priesthood has not been involved, I think that we can only conclude that possession is a possible and perhaps even probable cause of the aberrant behavior.