The 24-year-old was arrested following the death of a baby in the Intake area of Sheffield in the week before Christmas.
He has since been bailed.
South Yorkshire Police revealed over the weekend that officers were called at 9.54am to a house in Intake following reports from Yorkshire Ambulance Service that a baby was in cardiac arrest.
The baby was taken to hospital, where she later died.
In a statement, South Yorkshire Police said: “Police were called at 9.54 am on Saturday, December 18 to a house in the Intake area of Sheffield following reports from the ambulance service that a baby was in cardiac arrest.
“The girl was taken to hospital where she sadly died.
“Enquiries into the incident remain ongoing and a 24-year-old man has been arrested in connection with the incident and has been released on bail.”