<human>: I (38F)was friends with a troubled woman (40F)for a while until her toxic behavior became too much.  In the past she had lent me a bracelet and claimed it had not fit her, she said I could hold onto it for a while.  I recommended she sell the bracelet and purchase something she would wear, she told me I could keep it and it didn't matter to her. I asked her later if she was certain she didn't want it back and she said she was sure.  Months later, some of her behavior was getting toxic.  Eventually I drew the line and told her it wasn't acceptable, and we ended the friendship.  Months later, she emailed me and asked for anything she left at my house and for 'her' bracelet back.  I was accustomed to her changing history to suit her needs of the moment and reminded her of each event and conversation regarding the bracelet. I got a call from the police telling me they'd had a report of theft.  The bracelet wasn't worth a fight I wanted her out of our lives and I didn't want her to get any more of my attention.  I met her at the police station but she refused to withdraw the complaint. The woman working at the station said that it would be listed as 'returned' and that since I wasn't charged with a crime, it would not show up on a background check.

Can you summarize the given text in a few sentences?
<bot>: ex-friend wanted a gift returned and accused me of theft, If the police were contacted but I was not formally charged, will a complaint show up on a background check?