A man shot and killed a woman outside a San Pedro home late Friday, then turned the gun on himself, leaving him in critical condition, police said.

The incident occurred around 10:30 p.m. Friday in the 3100 block of Almeria Street, Los Angeles police Officer Rosario Herrera said Saturday.

The victim, identified as 45-year-old Michelle Stamper, and the suspect, 55-year-old Johnny O'Kane, had been dating, police said, and the two were involved in a dispute at the time of the shootings.

Police and neighbors said O'Kane chased Stamper out of the house and then shot her. Her body was found under a tree across the street, a neighbor said.

The man called police and said he shot a woman, said Officer A. Rodriguez of the Harbor Division.

Officers arriving at the home found the man inside with a gunshot wound to the head, he said.

Stamper was pronounced dead at the scene. O'Kane was taken to County Harbor-UCLA Medical Center in critical condition, Herrera said.

Neighbors on the quiet street said O'Kane had two children in their late teens or early 20s from a previous marriage.

The couple was described as quiet and friendly. One resident said the family had lived in the house for many years.

Several neighbors said they heard shots, but none of them could recall any incidents of violence at the residence.

Political signs were posted outside the small house, including several against state Proposition 30 and for Los Angeles Measure J.

A sign in the front window said, "We stand with Wisconsin workers."

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