It can be very difficult. A mental illness or mental health problem like DID/MPD (disassociative identity disorder/multiple personality disorder) can seem like demonic possession. However, if a person is demonically posssessed, then it would be diffcult for them to take part in communion or practice any beliefs where they had to declare their belief in Christ as their personal Lord and Savior.
A person with DID would be able to do all these things and more. Usually you can tell that a person has DID by a couple of symptoms:
1) They miss time and don't know what day it is when they 'return'; sometimes they are gone for minutes, days, weeks, and sometimes months and end up thinking that it's the same day/time it was when they 'left'.
2) They hear voices in their head, specifically, they can have entire conversations with the other voices in their head; the difference between a demonic posssession and DID in this case is the names of the other voices - for DID, you'll have normal names like Jack, Emma, Jimmy, Margaret, etc. - for demonic possession, the names will be like Lust, Envy, Pride, Deceit, Rage, Pederast, etc.
If you check on-line information about DID, schizophrenia, or bi-polar disorder, it'll help you figure out what the most likely possibility is.