HOUSTON, Texas -- The Houston Police Department confirmed Sunday that one person is dead after he shot his father and turned the gun on himself.

According to police, the shooting occurred at 3437 Ella Lee Lane at Larchmont Road in the River Oaks neighborhood of Houston.

The shooter was pronounced dead at the scene, police said.

The shooter's father was transported by the Houston Fire Department ambulance to Ben Taub Hospital in the Texas Medical Center, where he was listed in critical condition. He has since been downgraded to stable condition.

Houston homicide detectives are still investigating the shooting and said they are not ruling out but are not searching for a third party in connection with the shooting.

Neighbors told KPRC Local 2 that the father ran from the house bleeding and headed to a neighbors house to ask for help, saying he had been shot.

Neighbors also said a woman -- identified by neighbors as the victim's wife and shooter's mother -- came to the house late in the afternoon.