Nursing home no trespass.

If you are not visiting someone or have reason to be in the facility I would think they have every right to ask you to leave.
If you cause a disturbance or otherwise upset any resident they have the right to ask you to leave.
If you are a hinderance to staff they can ask you to leave.
If a person that is POA for a resident does not want you visiting they can ask you not to visit. If the resident does not want you or others visiting they can request no visitors.

Your statement is not a question so not sure what you are asking.

A nursing home, I would think can trespass you from the facility if you have caused somekind of disturbance that needed the police.

You don't ask a question. Please edit this post so you ask a question and provide context for your question. I don't think a NH can have a blanket No Tresspassing policy, but maybe an indivual resident's guardian or PoA can put someome on a No Visitation list, or have a Restraining Order against them enforced at the door.