Could a 17-year-old mother who lives with her parents obtain sole custody if the 20-year-old father of the child has a criminal history and lives in an unstable environment?

It is certainly possible. That being said, under the law an unmarried woman retains sole custody rights to a child unless a court rules otherwise. Custody, visitation, child support and other issues will not be addressed by the court unless parentage has been established. If the father has not signed the birth certificate or a declaration of parentage it will be necessary for him to establish his parental rights through a paternity test. The preferred method is DNA although a traditional blood test is acceptable in the majority of cases.