Thank you for your question
My name is Clare
I shall do my best to help you but I need some further information first
How old is the Child and when did you last see the child?
How do you know that she has reported you?
But you have not been approached by the Police at all?
When did you last see your daughter?
Since you have not been contacted by the Police there is nothing you need to do about the "allegations" she is making unless or until the police take action.
It actually seems unlikely that she has contacted the police at all.
So far as your daughter is concerned the law says that a child is entitled to ocntact with both parents and the courts will enforce this of necessary
You should make an application for a Child Arrangement Order setting out that time that you spend with your child using a Form C100 available here
The fe eis £215.
In addition you need to complete a form C4
and ask for an Order that the DWP release her address TO THE COURT for service
I hope that this is of assistance - please ask if you need further details
Sadly there is nothing you can do about what she may or may not have told a refuge.
Unless the Police become involved then there is no way that you can address the matter - unless of course your ex tries to apply for an Order forcing you to leave the matrimonial home which will open up the matter for you to defend