A four-year-old boy in US' Indianapolis city picked up a gun lying on a kitchen table and fired a shot that killed the three-year-old daughter of his father's girlfriend.

After finding the .45-calibre handgun, the boy pointed it at the girl's head and fired, police officer Jeff Duhamell of the Indianapolis metropolitan police said Friday.

The girl's mother, Fiona Lee, 26, was home at the time of the shooting and was arrested on charges of child neglect and drug intake after officers found cocaine and marijuana in the house, the Adelaide Now reported.

The boy's father Curtis White, who is Lee's live-in boyfriend Curtis White, is missing, police said.

Duhamell said it was not clear who the gun belonged to, but that White, 24, has a record for a handgun offence. Lee also has a similar record, he said.