Phone theft??

My ex roommate and I got into a huge argument and she moved out. Thing is, the phone I use was given to me from her. Her words "use it until you can afford a new phone" so that's what I'm doing. The phone is now underneath my parents phone bill and their names. So, my room mate went and said I "stole" the phone because she's pissed. Now a detective wants to meet and says he can charge me with theft if I don't give the phone back ASAP even though I DIDNT STEAL IT. Who is in the wrong here? Could I actually be charged with theft now that the phone is registered underneath my name and my parents? I don't know how that phone stuff works.. I don't see how they could considering people buy and sell used phones off the internet all of he time? Then just change it to their names? Couldn't anyone be considered a theif then if people really wanted to press that charge?!