For nearly three decades, they pursued her husband, Kazuyoshi, for the 1981 crime. But he remained beyond their reach, as Japanese authorities tried and convicted him of murder, only to see the case overturned.
When the break finally came last week, it was the result of Miura's own Internet-fed self-promotion: a personal blog.
Since 2005, police had been monitoring postings by Miura, who had become an outsized Japanese personality because of media coverage of his alleged crimes.
On one website, Miura promotes himself as a human-rights advocate who helps those falsely accused of crimes. He also publicizes his book and a DVD about his case and holds gatherings featuring alleged victims of wrongful prosecution and other guests, whom he charges about $30 to attend.
In postings last year, police said, he mentioned international travel plans, including a possible trip to Saipan, a U.S. territory and popular tourist destination north of Guam.
Retired LAPD Lt. Jimmy Sakoda, who worked with Japanese authorities during their prosecution of Miura, had maintained contacts with his international counterparts, according to Det. Rick Jackson of the LAPD's Cold Case Homicide Unit.
After Sakoda gave Jackson a heads up about Miura's travel plans, detectives alerted Immigration and Customs officials in Saipan to be on the lookout.
They apparently missed his arrival, but immigration agents on the island nabbed Miura, now 60, last Friday when he attempted to leave for Japan.
"It was just a matter of wait and see," Jackson said of the final push to catch Miura, "if he left [Japan], and whether things would work out with our liaisons in other countries."
Miura, who has repeatedly denied involvement in his wife's murder, is awaiting extradition to Los Angeles.
LAPD detectives say they have a strong circumstantial case, built on evidence they helped prepare for the prosecution that initially succeeded in Japanese courts. The arrest and trial to come will bring the long, twisting saga -- a Japanese version of the O.J. Simpson case, featuring allegations of a hit man, a conspiracy with a former adult actress and a $650,000 life insurance policy -- back to where it began, and back into the media eye.
At Los Angeles police headquarters Thursday, detectives were briefing a Japanese television team on the case. Twelve more camera crews waited in the lobby.
It was about noon in the fall of 1981, Kazuyoshi Miura said, and he was snapping photos of his young wife Kazumi on Fremont Avenue, beside the Harbor Freeway, when she fell to the pavement, apparently shot in the head. He said that as he ran to her, he felt his left thigh burning and realized he also had been hit.
Then a stylish, ocean-hopping importer, Miura claimed that two men in their mid-20s appeared and casually rifled his pockets and his wife's purse, taking $1,200 before driving off in a large, dark green older car.
"Without any contact or asking, they just started to shoot," Miura told a Times reporter from his hospital bed. "To do this, just for $1,000. What is this all about?"
He blamed America's culture of violence and said he would write protest letters to the president, the governor and the mayor. "Many Japanese will be coming to the U.S. with a dream on their hearts. I strongly hope this accident will never occur again," he told one group of reporters.
The .22-caliber round that struck Kazumi left her in a coma for a year. The U.S. Air Force flew her back to Japan, where she died in November 1982.
At first, Kazumi's death appeared to make the case that no one was safe in Los Angeles, then struggling to control drug and gang violence. But as L.A. police and Japanese reporters dug deeper, darker details began to emerge. There had been an attempt on her life three months before she was shot.