Nobody has been charged with the death of a toddler despite medical experts agreeing the little girl's injuries were not caused by accident, an inquest has heard.
A detective confirmed that the Crown Prosecution Service (CPS) decided no-one could be prosecuted over 21-month-old Summer Rogers's death because it could not be established whether it was her mother, step-father or grandmother who was looking after her at the time she was hurt.
Detective Constable Richard Peckett told the inquest in Bradford that Summer's mother, Victoria Rogers, had been arrested on suspicion of murder during the investigation into her daughter's death, along with her grandmother, Susan Rogers, and her mother's partner, Craig Sharp.
He said West Yorkshire Police submitted a file to the CPS but there was no prosecution.
The detective said this was because all three of those arrested had looked after Summer at her home in Dewsbury at some time in the early morning of February 27, 2012, but pathologists were unable to pin-point exactly when the injuries were sustained.
Assistant Deputy Coroner Oliver Longstaff asked Mr Peckett: "The sticking point for the prosecution was not that there was some doubt whether there had been an unlawful act?"
He said: "They certainly opined that there was a non-accidental head injury."
The coroner said: "The sticking point was the difficulty in establishing how that had been caused?"
Mr Peckett added: ".....and who had caused it."
The coroner said: "In broad terms, there were set times within the early morning of the 27th when each of three people had some involvement in being responsible for Summer?"
The officer agreed.
Mr Peckett said the three people who were arrested had first been interviewed as witnesses following Summer's death. But they were arrested later when expert medical reports were made available to the investigation team.
Bradford Coroners Court was told how Summer was a normal, healthy child in a family with no involvement with social services.
She lived in Nook Green, in Dewsbury, with her mother, an auxiliary nurse and Mr Sharp, a garage manager.
Her only injury worthy of hospital treatment until her death was an unexplained scald to her hand which, the court heard, was probably caused by an accident.
Pathologist Matthew Lyall said he had been told before conducting the autopsy on the little girl that the alarm was raised on the morning of February 27 by Summer's grandmother, Susan Rogers.
Victoria Rogers and Craig Sharp had also been involved in her care earlier that morning, the court heard.
Dr Lyall confirmed that Summer died from a blunt force injury to her head.
He said this would have "necessitated more than a trivial impact" and also said he could not say whether it would have been caused by an object or a surface, such as a wall.
Dr Lyall said he excluded an accident because the trauma was so severe that it could not have gone unnoticed by the adults around her.
Victoria Rogers watched the proceedings in the court along with many other members of Summer's family.
The inquest was adjourned until Tuesday when more expert evidence is expected to be heard.
It is due to last six days.