Philip Peace, aged 42, from Himley Road in Dudley, is accused of killing five-month-old Summer on September 9, 2017. He has denied this.
He is alleged to have shaken Summer before she collapsed and suffered fatal brain injuries, prosecutors allege.
The trial is nearing the end of its course where closing speeches are being heard from Peace’s defence counsel at Birmingham Crown Court.
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Michael Turner, the defence counsel for Peace, asked jurors: “Did Mr Peace really shake Summer to death? Why are there no fingertip bruises to indicate he did so?”
Once the cases have been finished by the prosecution and the defence, jurors in the trial will be tasked with deciding whether they think Peace is guilty.
They have heard a range of evidence including medical reports.
Jurors were previously told that Summer turned blue due to a lack of oxygen.
Peace called 999 after noticing something was wrong with his child, jurors were told.
He administered CPR before paramedics arrived about three minutes after the emergency call, the court was told.
Summer, who was struggling to breathe, was treated by paramedics – who tried to clear her airways and later put an oxygen mask on her – at the scene and en-route to Russells Hall Hospital before she was transferred to Birmingham Children’s Hospital.
It was later established she couldn’t recover from her injuries and it was agreed her life support would be withdrawn.
She died at 5.44pm on September 9.
Peace, who was interviewed twice by police, said he couldn’t recall any event which had caused or contributed to her death.
The trial continues.