I suspect that the court you refer to is a probate court. Mental health law is primarily administered by probate courts and handled by probate lawyers. Therefore, I am editing the practice area you selected so you will receive answers from probate lawyers. As I am not a probate lawyer, I am not competent to answer your questions.
One thing I think I can safely tell you is that the legal process you inquire about is anything but simple and straightforward. Although you can get some useful information here, you will almost certainly need to hire a probate lawyer to accomplish whatever your relative needs done.
I think you are talking about the mental health court that begins when a mental health warrant. If that is not correct, then disregard and re-ask your question.
If the patient has been confined on a mental health warrant, if the hospital finds that, after medication, the patient is stable and competent, the patient will be released. I do not think the release requires another court hearing. Any court hearings are public, unless the patient specifically requests a closed hearing. If there are court hearings, the patient is provided an attorney at County expense.
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