By Bill Mears, CNN Supreme Court Producer

Washington (CNN) - A custody battle involving the "best interests" of a 3-year-old Cherokee girl will be taken up by the U.S. Supreme Court, an issue spanning the rights of adoptive parents and the desire to preserve Native American families within tribes.

The justices announced they will hear an appeal from Matt and Melanie Capobianco, who legally adopted little Veronica in 2009, shortly after the birth mother agreed to give up the child. Oral arguments in the case will likely be heard in April with a ruling by late June.

The South Carolina Supreme Court in July ruled for the biological father, who had sought custody shortly after the child's birth. He is a registered member of the Cherokee Nation and is raising the child in Oklahoma.

Dusten Brown had earlier signed a legal document agreeing to put the girl up for adoption, but his attorneys say the father did not understand the extent of the waiver, and that the birth mother misrepresented the child's American Indian heritage to social service workers when the adoption was finalized.

At issue is whether Brown, as the onetime non-custodial father, can gain parental custody, after the non-Indian mother initiated an adoption outside the tribe.