Detectives launched a murder probe yesterday following the death of 22-month-old baby girl at Sheffield Children's Hospital and arrested a 19-year-old man on suspicion of murder.
They were granted an additional 36-hours to question the man by magistrates in Sheffield this morning.
A police spokesman said the post-mortem examination carried out last night revealed a cause of death of severe head injuries.
The baby died just before 12.30am on Tuesday.
Neighbours on Leighton Road, Gleadless, described seeing the baby being carried on a stretcher with head injuries.
Senior investigating officer, Det Chief Inspe Steve Whittaker said: “The death of a child is an undeniably harrowing and traumatic event.
“While I fully appreciate this incident has stirred an understandable, emotional reaction from people, the family need to be able to grieve for the loss of the child, at such a devastatingly young age, and I would ask people to please think about the impact that speculative comments on social media could have on them at such a heart-breaking time.
“The investigation is in the very early stages and we must ensure we comprehensively conduct all enquiries to ascertain the exact circumstances and facts in this case.”
Anyone with concerns or information should call police on 101, quoting incident number 356 of May 21.