No, you need notarized consent from one parent or guardian. You can also get a waiver from the court in case you have reasons not to get your parents involved. Ask about that at the clinic.
It depends on the state in which you live. However, an abortion is a serious procedure and your parents should know that your health is being compromised by such, just as if they have the right to...
You might need a signature but it's also illegal to force anyone to go through an abortion against their will or to have a baby against their will. You are the the one who decides what will happen...