There is no absolute contraindication for telepsychiatry and virtually any mental health condition can be treated via telepsychiatry. Generally, the concerns about psychotic patients becoming more paranoid or distrustful with telepsychiatry are overblown.
However, in rare cases, a patient may not be appropriate for telepsychiatry if they are truly fearful about a delusion that involves the camera or videoconferencing equipment. Does this mean that telepsychiatry is inappropriate or impossible to effectively treat such as patient? Not necessarily...
It is important to remember that psychotic patients can incorporate anything from their environment into their delusional beliefs. For example, a patient may be delusional that they are being held captive in a secret Nazi prison camp. This does not mean that they should be discharged from the unit out to the street. Likewise, a patient who has delusions about telepsychiatry does not necessarily fail to benefit from telepsychiatry.
Nevertheless, it is theoretically possible for a patient to be so paranoid about telepsychiatry that they become mute or refuse to participate in the telepsychiatry session. If that same patient is willing to converse with a psychiatrist in the facility, then perhaps onsite psychiatry may be a more effective option. This would be a clinical decision based on the case factors. Ultimately, if the treatment team feels that the patient fundamentally cannot benefit from telepsychiatry due to their delusional beliefs about that modality of care, then other arrangements should be made to provide care onsite.
In summary, there are certain clinical situations where a patient's mental status or condition may require that arrangements are made for onsite psychiatric care. However, this happens very rarely. Overall, telepsychiatry is an effective option in the vast majority of mental health cases.