The Western Australia's Department for Child Protection and family support has been made aware of police information over "allegations of the father's criminal background" in the case involving Down Syndrome baby Gammy.
A spokesman told the BBC: "Last night we were made aware of certain information by the police regarding allegations of the father's criminal background."
More top news
Father Jacques Hamel has been described as man who dedicated his life to his parishioners and still regularly led mass, even at 86.
Rain will spread southeastwards through N. Ireland, Wales and England overnight.
The woman used her daughter's own Facebook page to live-stream the attack after the teenager posted provocative pictures online.