A woman was shot and killed in a carjacking in downtown Seattle on Wednesday morning, less than an hour after four people were killed and one person was injured in a shooting near Cowen Park in North Seattle, the Seattle Police Department said.

Police said Wednesday afternoon evidence had led them to believe the separate killings were connected.

Police said in the downtown shooting, witnesses heard a man and a woman fighting in a parking lot just west of Town Hall near 8th Avenue and Seneca Street. The woman called for help and the man pulled out a handgun and shot her in the head.

"I was like one of the first to get up to her, and this guy, he's putting his palm up -- 'don't go, don't go' -- and I just go up and just look at her, and she's shot in the face, obviously," witness Chelsy Clark said.

Joann Stremler, another witness, told police more about the attack.

"My window was down, and I see this guy leaning over this woman, kicking her, and then he shot her in the face," she said.

KIRO 7 is not revealing the woman's name at this time, but her family confirmed she was an innocent victim in the rampage, confronted by a man who apparently wanted to take her car.

"She was on the side of her car," Clark said. "I think she was walking to her car and I think he mugged her, pretty sure."

Police said the man took off in that car, a black Mercedes SUV, which was later found in West Seattle with a handgun in the driver's seat.

Police searched the area, near the 4100 block of Delridge Way, for the suspect.  By 2 p.m., police said they believe the suspect had left the Delridge area.

Officers suggested the man may have boarded a bus, but King County Metro said it didn't believe that was true and officers were talking to a bus driver to find out if anything suspicious was seen along the route.

Late Wednesday afternoon, police confronted a man in West Seattle who matched the description of the man in the Roosevelt shootings. Police said the man knelt to the ground and shot himself in the head. He was rushed to Harborview Medical Center and later died.