How can I sign my parental rights on my troubled teen daughter who is constantly putting my other kids in dangerous situations and who also is constantly getting in trouble @ home/school... she lies (for no reason), steals, very disrespectful to adults, fights at home/school, having sex at home/school, and is constantly running away leaving my window open where anyone can enter my home... because we are asleep... she has an I don't CARE ATTITUDE towards anyone and everything... I have ran out of options, and don't know what else to do because I'm not getting any type of help from the local police/sheriff department...

Do you mean sign away parental rights?
What state, if the US?
There are some laws regarding 'incorrigible children' in some states.
But overall, you are responsible for any child of yours until 18. A child in trouble will have plenty of contact with police after 18. You need to handle this, and that would have involved social services and schools.

Is she 15 or 11? (I will edit the title to be clearer.)