The North Buckinghamshire coroner, Rodney Corner, heard that police were satisfied that Hannah Dawn Davies, of Oldbrook, Milton Keynes, had died as a result of an accident and foul play had been ruled out.
Det Chief Insp Stan Horlock said a 3 1/2 -year-old boy had been interviewed in the presence of his mother about Hannah's death last Wednesday at the Oldbrook playgroup.
Mr Horlock said there was 'a connection' between the actions of the older child and the death of the baby, but he added: 'It is believed death was caused by accident to the child.'
The inquest at Milton Keynes heard that Hannah's mother, Virginia Davies, 24, had taken her with her brother and sister to the playgroup at about 9.30am. Mrs Davies's eldest child attended the playgroup and she was also due to help out that day.
Hannah, who was in her buggy, was placed in an office at about 10am and left with the door shut so she could sleep. At about 11.30am a member of staff went into the office and found Hannah out of her buggy, lying face down on the floor, Mr Horlock said.
'The child had not been strapped in. She was a small child. It was sufficient to place her in the buggy,' he said.
Hannah was taken to Milton Keynes General Hospital where, despite efforts to resuscitate her, she died at 12.08pm the same day.
First indications were that death had been caused by severe head injuries, the inquest was told. The other child involved in the incident was not named.
Mr Horlock, who said police had carried out exhaustive and extensive inquiries into the incident, added that Hannah's parents had felt unable to attend the inquest, which was yesterday adjourned until 21 July.
The coroner, issuing a cremation certificate, offered his 'deepest sympathy' to the parents of the dead child.
After the hearing, Karen Caldbeck, the playgroup's chairwoman, issued a statement saying: 'We are all deeply saddened about this tragic accident and our sympathies are with both families.'