Poppi Worthington died in hospital in December 2012
A 13-month-old girl was sexually assaulted by her father shortly before her sudden death, a judge has found.
Poppi Worthington, who was found with serious injuries at her home in Barrow, was pronounced dead when she was taken to hospital in December 2012.
Her father, Paul Worthington, 47, was arrested and questioned on suspicion of sexual assault but never charged with any offence. He denied any wrongdoing.
A later inquest took just seven minutes to declare the death "unexplained".
High Court family judge Mr Justice Peter Jackson, sitting at Liverpool Crown Court, ruled that - on the balance of probabilities - Mr Worthington "perpetrated a penetrative ... assault on Poppi".
Poppi Worthington's father Paul has denied any wrongdoing
The death of the toddler had been shrouded in secrecy with a 2014 fact-finding civil court judgement being kept private so as not to prejudice any criminal proceedings.
Last month, three medical experts gave evidence in open court stating they disagreed with the findings of a Home Office pathologist who believed Poppi was the victim of "a penetrative sexual assault".
In his judgement, Mr Justice Jackson said he could not accept Mr Worthington's evidence relating to the collapse of Poppi at the family home and was "not impressed" with his account of the events leading up to her death.
On 12 December 2012, Poppi awoke screaming at around 05:45 GMT, according to her father, and an ambulance was called.
On admission to hospital and at post-mortem the youngster was found to have an earlier fracture of her right lower leg and other suspected acute injuries.
The youngster was buried in February 2013, precluding a further post-mortem examination, after her body was released by then local coroner Ian Smith.
Cumbria Police announced in March last year that no charges would be brought against anyone over Poppi's death.
Lawyers representing Mr Worthington, who was not in court for the latest judgement, had told Mr Justice Jackson he was a "doting and loving" father and there was "no sufficient evidential basis" to suggest he abused his daughter before her death.
BBC Correspondent Fiona Trott at Liverpool Crown Court
Based on medical evidence, Mr Jackson believes Poppi's father sexually assaulted the toddler before she died. But what happens next?
A new criminal investigation needs fresh and compelling evidence.
Paul Worthington was previously questioned by police and no charges were brought. He denies any wrongdoing.
The judge has also criticised the way Cumbria Police and Cumbria County Council investigated the case, adding neither Poppi or her family "received the professional response to which they were entitled".
Mr Justice Jackson said: "Careful assessment of the meticulous pathological and paediatric evidence has clearly established that [Poppi's] injuries were the result of trauma from outside the body.
"My finding (in the previous judgment) was that the father perpetrated a penetrative ... assault on Poppi ... That remains my conclusion."
It emerged previously that senior detectives thought pathologist Dr Alison Armour "may have jumped to conclusions" when she raised suspicions about Poppi's death as they decided not to investigate until the full post-mortem report was ready - but it was not finished until the following summer.
The Independent Police Complaints Commission (IPCC) is reviewing how Cumbria Police conducted its investigation into Poppi's death.
It has already emerged that officers failed to preserve vital items for forensic analysis, either at the home or at the hospital after Poppi's collapse, and the scene at the house was not properly secured.
Mr Justice Jackson was sitting at Liverpool Crown Court
The IPCC is due to present its findings following a second inquest into the youngster's death, which is yet to be held.
Responding to the latest judgement, a Cumbria Police spokesman said: "The Constabulary are fully aware of Mr Justice Jackson's criticisms of the initial investigation and have assessed these.
"One officer was suspended and has since retired, another two were moved into different roles. One of those officers is currently undergoing performance proceedings and the second officer has been dealt with by management action.
"The Constabulary will support any future inquest or hearing into this death and have cooperated fully with the IPCC investigation.
"Whilst performance proceedings are active and an inquest is to be held we are unable to comment any further."
Mr Worthington, who claimed that his daughter could have died as the result of a viral infection, was informally interviewed by police in 1995 over his association with someone who may have committed offences against children and, in 2003, was the subject of an unrelated allegation which was later retracted.
It also emerged that he watched pornography on his laptop in bed in the hours before Poppi's death, which he described as "involving adults".