As it stands, students can drop out of high school at 16 years old.
In recent years, the North Carolina General Assembly gave the OK to two North Carolina districts to change their drop out age to 18. State educators say in those districts the dropout rate decreased and the graduation rate increased
So she can drop out with out your permission. But you can set some guidelines of what will happen in your home. Will she have to work on GED? Move out? Get a job? PAy rent?
Probably best to be supportive, but have some guidelines in place if she decides she wants to move back in the future, plus have a discussion about what you are willing to be financially responsible for. Will she stay on your health insurance? Does she have a car in her name? Car insurance? I would not want my adult child to take a car in my name and live elsewhere, because of the liability issues.