Minnesota Statutes define who is a minor and who is an adult at MN Statutes § 645.451. Generally, being "emancipated" means that a minor has the same legal responsibilities as an adult. Minnesota Statutes do not specifically define a process by which a minor can become emancipated.
Courts will review "Petitions for Emancipation" and decide on a case-by-case basis if there is sufficient evidence to find that a minor may live "independently" of his/her parents or guardian. However, the courts do NOT publish forms or instructions to petition for "emancipation." The Legal Fact Sheet on Emancipation explains the basics on this area of law. To get legal advice on your situation, you should talk with a lawyer.