Hello, I would like to know what my legal rights are when my 16-yr-old teenage daughter has moved out?

In what way? Your daughter doesn't have the right to move out as a minor. Where is she going, who is she going to live with? Please expand on what you need to know and the situation so we can help.

With parent consent, a child can live without parents at the age of 16.

Sorry no, a 16 year old would have to be emancipated, at least in the US.
In 2 states ( that I know of ) a 17 year old can move out. ** excepton would be to be married with parent permission
A 16 can not sign a contract, can not rent a apartment, can not get electric in their names and so on.

So the parents have the right to call the police and have the child dragged home.

With parent consent, a child can live without parents at the age of 16.

Even if that were true (which it isn't) There is no indication here that she has parental consent.

Sorry maybe it was 17

Hello, I would like to know what my legal rights are when my 16-yr-old teenage daughter has moved out?Hello Bolanie:

You don't have any rights in the matter. You only have obligations and liabilities. You are liable for any damage she causes to others property. You are responsible for feeding her and clothing her and making sure she has a roof over her head.

Even if she's 17.

excon