Want to know what steps are required to have someone involuntarily committed to a mental hospital in Georgia? Person is adult and has chronic depression, etc and has recently threatened to kill himself and his minor daughter. I am a very concerned family member living in Alabama, as are his other close relatives.

Below is a link that should be of service to you.I am sure they can point you in the right direction.
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The rules vary from state to state. Generally, you must petition the local magistrate's office and sign an affidavit stating the facts that show this person is a threat to himself and/or others. From what you have said this person meets the criteria--a history of depression/mental illness and threatening suicide and homicide. Suicide and homicide are against the law, as is communicating a threat.
The magistrate determines if there are reasonable grounds for committal and if so, a custody order would be issued and an officer would pick him up and take him to an appropriate place (hospital or psychiatric hospital) where he will be held and examined. But, you are out of state... I wonder if your local magistrate's office would be able to give you guidance or if the agencies can work together?
I wish you all well.