Bradford takes the folded piece of paper with Wright's phone number on it as Wright is handing it to Chen. As Wright walks away, Bradford crumples the paper up in his fist. When Chen sticks her hand out asking for the paper, Bradford then hands it to her and it's crisp and uncrumpled.
Lucy Chen did not identify herself as a police officer before placing the bar thief under arrest. She does eventually, but not until after she has the suspect in handcuffs.