The case emerged during testimony of a 57-year-old woman at the Historical Institutional Abuse (HIA) inquiry.
As a young girl, she was put into the care of nuns at Nazareth House in Belfast on a number of occasions.
The inquiry heard she was returned to her parents, despite the authorities knowing that she was being sexually abused in her family home.
The girl was subjected to "serious physical and sexual abuse" at her home, the inquiry heard.
Joseph Aiken, counsel to the inquiry, said her statement outlined "very difficult home circumstances that characterised your initial few years of life".
"Your parents were known to the authorities, had been to court and the difficulties continued despite that," he told her.
In her statement, the witness asked: "Given that I was put back to my parents and abused again by my father, how did that come to pass?"
The Health and Social Care Board has undertaken to examine the circumstances of the case.
The woman also claimed that she was subjected to cruelty by two nuns during her time in care.
The HIA inquiry is currently examining abuse claims at Nazareth House and Nazareth Lodge.
The homes were run by the Sisters of Nazareth, who have made an apology to all in their care.
The inquiry was set up in 2013 to investigate child abuse in residential institutions in Northern Ireland over a 73-year period, up to 1995.
Social services in Northern Ireland have agreed to examine the handling of a child sex abuse case in the 1960s.