Accused of Identity Theft by an Ex-Girlfriend

My ex gf when she moved out said i could keep the electric bill in her name. She lived with me and my parents . her and my dad handles those bills. she now has accused me of ID theft. But today when we got called in for our statement the detective only had my dad fill out a report and sign it not me. Does that mean now they are focusing on him instead of me?
In the report i was the person on interested but they had me fill out no paper or statement or sign anything which seemed odd to me
the dect then said she would call my ex back and tell her our side.
live in florida

It is not clear why your parents would need to put any of their utility bills into your ex-girlfriend's name. It's also not clear why this is now an issue, unless they haven't been paying the bill that is in her name. Perhaps you could explain. You also need to be clear on exactly what it is that your ex-girlfriend is denying. Does she deny ever giving permission to place the bill in her name, or is this over the failure to move the bill out of her name, the failure to pay the bill, or both?

If in fact it was not you who was given permission to put the bill into your ex-girlfriend's name, or who failed to remove the bill from her name when she moved out, but was your father, then that would explain the police focus on dad. Dad should stop talking to the police and start talking to a criminal defense lawyer.

She agreed to have them in her name because the deposit was less and since she paid no rent or nothing for food she said it was ok to put them in her name.
When she moved out she said to change the cable and the water bill but it will fine to keep the electric in her name.
Now she claims that we reinstated everything in her name after she moved out which there is proof that that isnt the case. She only named me in the case but after talking to us the Dect only had my dad write out a written statement and sign it not me
So i guessing the focus is on him now or they wouldve took a statement from me and had me sign it.
She is doing this now because for some reason her income tax refund is being held