Toddler Poppi died from asphyxia and was sexually abused before her death, according to the coroner David Roberts.
Mr Roberts formally referred a copy of his decision, made on the balance of probabilities, to the Crown Prosecution Service (CPS) on Tuesday.
A spokesman for the CPS said: “We have received a copy of the coroner’s decision and will now consider this carefully in liaison with Cumbria Constabulary.”
Mr Roberts said the child’s ability to breathe was compromised by an “unsafe” sleeping environment after her father Paul Worthington took her from her cot and placed her next to him in his bed.
He said 13-month-old Poppi was suffering from an upper respiratory tract infection at the time and she was abused in the bed.
The CPS has previously said it did not plan to review its decision not to charge Mr Worthington.
At Kendal Coroner’s Court, Mr Roberts concluded she did not die immediately after the abuse in 2012 and it did not cause her death.
The coroner said an unlawful killing conclusion was not available to him as he was not satisfied beyond reasonable doubt that Poppi died due to murder or manslaughter.
During a three-week inquest in Cumbria, Mr Worthington refused to answer questions about her death 252 times and his account did not “stand up to scrutiny”, according to the coroner.
A family court judge ruled in January 2016 that “on the balance of probabilities” he had sexually assaulted Poppi before she died.
More from Poppi Worthington
The father has denied any wrongdoing and has not been charged with any offence as the CPS says there is insufficient evidence.
He has been living in hiding since the family court proceedings were made public.