Thank you for your question.
A person can be held against the person's will if there is a reason to believe the person could be an imminent danger to herself or others.
I suspect that your daughter did not fully meet the guideline of an imminent danger but the counselors were concerned enough to not want to release her. This may be why they convinced you to sign her in.
Now that you have signed her in, the hospital apparently cannot release her until they determine that she is not a danger to herself or others.
I hope that the information which I provided was helpful to you.
Best wishes for a successful outcome. If you have additional questions, please do not hesitate to submit them to me directly.
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THIS IS FOR INFORMATION ONLY. NO ATTORNEY-CLIENT RELATIONSHIP EXISTS. PLEASE CONSULT A LAWYER IN YOUR STATE FOR LEGAL ADVICE