Poppi Iris Worthington died in December 2012 when she was 13 months old.
A 46-year-old man and a 30-year-old woman have been arrested in connection with the death and are on conditional police bail until December.
The initial police investigation is being probed by the Independent Police Complaints Commission (IPCC) and an officer has been suspended.
Cumbria Constabulary is continuing to investigate the death, but the IPCC is investigating several officers.
The coroner for south and east Cumbria, Ian Smith, told the inquest there had been a two-week Family Court hearing into the death, which found the cause of death could not be ascertained.
He said it would be inappropriate for another court to come to a different conclusion and recorded an open verdict.
The death of a baby girl in Cumbria, which has led to two arrests, cannot be explained, an inquest has found.