Mandy is correct. It is inappropriate. There may be no intention to be sexually active during the night but temptation happens and sometimes people make poor choices they never intended to make. It also puts the girls reputation in questions and shows no respect for her, her parents, or your parents.
You cant and you shouldnt. There is absolutely no reason for a teen to have a boy or girlfriend spend the night with them, at all. When your an adult and live under your own roof you can have all the opposite sex sleepovers you want....but for now your just a kid.
I think mandy's answer is kind of dumb, because teens could have the opposite sex sleep over, it's just depends on the amount of trust you have between you and your parents. They think you just want to have sex with her, and you have to show them you wont.