Is it possible to have guardianship of my sister and how do I go about doing this?

I'm wondering about how to go about obtaining guardianship of a teenager. She is currently 15 years old and my little sister. She is in her father's care, however he is ill and I fear may be passing. If she were to go back to live with our mother she would be in danger since my mother's boyfriend attempted to molest her and he was found guilty of these accusations with a sentence of probation. I want to obtain guardianship of her once he goes. I live in Connecticut and she lives in New Hampshire, therefore she would also be moving out of state.