The police have discretion on this.
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Typically, an arrest is questioned or determined if valid only after it is challenged in court. So in most cases, even illegal arrests are never challenged. Police undergo training as part of their work to know where the line is, to the extent there is one, in determining if they can arrest a person. Also, remember that police have tremendous discretion in arresting someone, so even if they can, the sometimes won't. This is the initial filter built in to the criminal justice system to avoid or remove people from the criminal pipeline.
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The police typically give a summons for this arrest unless the person has a bench warrant in which case they are required to make an arrest.