Three-year-old girl's brother 'could have accidentally killed her with shotgun'

Police are investigating whether a toddler's brother could have accidentally discharged the shotgun that killed her as their father broke down in court and begged to see his little girl "one more time."

On Sunday night, the three-year-old's mother ran screaming from the Lalor Park house in Sydney's west before the father was charged with possessing an unregistered firearm.

The little girl suffered a fatal blow to her neck and officers are now trying to determine who discharged the weapon.

Police have tested the girl's brother for gun residue and are awaiting results from forensics.

On Friday, the family burst into tears at Blacktown Court and the father hysterically called for his daughter.

"Let me see my daughter one more time, please. I beg you. I'm so sorry. I'm so sorry," he said.

Outside court, the man's lawyer, William Barber, said he had never seen a client in "such a bad way."

"He has not slept for five days, he hasn't had medication for five days and I was unable to get instructions," he said.

"This is a tragic accident of epic proportions."

The father will be mentally assessed and could be moved to the care unit at Long Bay Jail.

He was already facing drugs and fraud charges.