Lilly's parents Stephanie Moreton and Craig Taylor said they were relieved to have their daughter home
A one-year-old girl fell from a first-floor window left open by a council worker, her parents have claimed.
Lilly Taylor suffered a cracked skull and a brain bleed during the accident in Tipton last Thursday morning.
Parents Stephanie Moreton and Craig Taylor claim a worker who had been repairing a window in the room Lilly was sleeping in forgot to shut it.
Sandwell Council deputy leader Mahboob Hussain said it would look at whether procedures were followed correctly.
West Midlands Police have also been looking into the circumstances of the fall. No-one has been arrested.
Lilly fell from the first floor of the couple's house (pictured right) last Thursday
Lilly underwent brain surgery at Birmingham Children's Hospital
"I know the council are at fault," said Ms Moreton.
"I put her [Lilly] down to sleep in that room - there's no way I would have opened the window."
Lilly was in intensive care at Birmingham Children's Hospital for two days and needed almost 60 stitches.
Ms Moreton, 21, said the alarm was raised by a neighbour who knocked on the door of their home in Highfield Road to say Lilly was lying on the floor in their back garden.
"I went around the back and saw her lying there," she said.
"She was not breathing and I just started screaming. 'Call an ambulance', I was shouting. We were both in shock."
Lilly's parents claim a worker had been repairing a window in the room she was sleeping in and forgot to close it
An air ambulance was called but logistical difficulties meant Lilly was taken to hospital by road.
The couple said the experience had been "devastating" but they were relieved to have their daughter back home.
"While she was in hospital we could not rest. We're told she is lucky to be alive," Ms Moreton said.
"No parent should have to go through it," said 26-year-old Mr Taylor.
He said Lilly, who has a three-year-old brother, was making a good recovery.
"Now she is happy, bubbly, back to her old self. She is one lucky girl," he said.
Lilly was in intensive care for two days
Mr Hussain said he was pleased Lilly was out of hospital.
"The matter has been referred to the police who are looking into it and we have no further comment to make at this time," he said.