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In my experience, criminal trespass has worked in this manner. Someone is ask to leave a property. They comply and come back later. The owner calls the police. If the individual is still there, the owner issues a criminal trespass warning in the presence of the officer. The officer should make a report and provide the owner with a case number. If the individual returns, the owner calls police, gives them the case number and the individual goes to jail.

If they do not leave initially, the process is shortened.

Criminal trespass with a weapon would most likely work the same way.

If they refuse to leave with the officer there, they are arrested then and there.