Dad charged after girl, 3, found shot dead

The mother of a three-year-old girl shot dead in their Sydney home has blamed the child's father, screaming that he shouldn't have had a gun in the house.

"Not my baby girl, not my baby girl," the mother screamed as she raced from the Lalor Park home into the street on Sunday night, neighbours recalled.

"I hate you."

It's unclear how the girl sustained the single fatal gunshot wound, but police are investigating whether she accidentally fired the weapon herself.

Neighbours spoke of hysterical scenes after the shooting.

"The mother came out, she was ... really angry. And she was just screaming," the neighbour Mark Tapua told reporters on Monday.

"She was just saying it was his fault, he shouldn't have had a gun in the house."

The girl's father, who emerged from the house covered in blood, was charged on Monday with possessing an unregistered sawn-off shotgun and not storing the weapon safely.

The 43-year-old Arncliffe man, who did not live at the house, was also charged with contravening domestic violence orders.

"When police arrived ... they found the child had suffered a fatal wound to her neck," police Superintendent Paul Carrett said.

The mother and daughter and three other children, aged between three and eight, had been in the house at the time.

The father appeared before Blacktown Local Court on Monday and did not apply for bail and it was formally refused.

He is scheduled to appear before the same court again on Friday.

Television footage from the scene showed a woman, thought to be the mother, screaming "I hate you... may you rot in hell", as she was taken away in an ambulance, while a man was sitting in the gutter with his head in his hands.