Jane Bell was on holiday with her family when she was rescued from the water. She died in hospital nine hours later.
Blackpool Coroner Alan Wilson adjourned the hearing for two months and said that Lancashire Police must provide him with a report on their investigation into the death in that time.
Outlining what happened at the Dalmeny Hotel, in St Anne's, Lancashire, on August 14 the coroner said the Bell family from Tweed Avenue, Galashiels, were holidaying at the Dalmeny which has an indoor pool.
The family had breakfast and went to the pool area.
He said: "In due course family members looked at the bottom of the pool and saw Jane. She was rescued from the water and taken first to Blackpool Hospital and then the specialist children's unit at Manchester Royal Infirmary."
The girl died nine hours later and her body later was identified by her father, David.
The inquest heard that Lancashire Police had contacted the coroner and said there was an ongoing investigation into Jane's death.
Her mother Sarah has been arrested and questioned on suspicion of murder and child neglect.
She is now on police bail.
The coroner said: "it is appropriate these proceedings are adjourned to see whether any criminal proceedings go ahead. During the intervening period I require the police to send me a report of their investigations."