SAN FRANCISCO (CBS/AP) — The parents of a woman murdered by a Los Angeles police officer in 1986 have lost their last attempt to sue the department over the way it handled the high-profile investigation.

The California Supreme Court refused to take up the appeal of Nels and Loretta Rasmussen, upholding a lower court’s ruling that the couple waited too long to file the lawsuit.

The Rasmussens sued the Los Angeles Police Department in 2010, 24 years after their daughter, Sherri, was found beaten and shot to death in the Van Nuys townhouse she shared with her husband.

The day after their daughter was murdered, her parents told investigators they suspected a jealous officer on the losing end of a love triangle.

LAPD Det. Stephanie Lazarus had previously dated Sherri’s husband, John Ruetten.

The victims’ parents badgered police, telling them that Lazarus had stalked their daughter and confronted her in the weeks before her murder.

“The only person that I could think of was John’s ex-girlfriend,” Nels told “48 Hours”.

Investigators rebuffed the parents and concentrated their efforts on two supposed robbers. That theory was debunked in 2005 when a bite mark was discovered on the victim and the DNA left behind was found to have come from a woman.

In 2009, Lazarus was arrested for Sherri’s murder when the DNA found at the crime scene matched hers. The Rasmussens sued the LAPD, alleging that its officers handling of the case caused them emotional distress, especially investigators’ refusal to take their claims about Lazarus seriously.

A trial court judge and then an appeals court both reluctantly tossed out the couple’s 2010 lawsuit as being filed way too late. The courts ruled that even the most liberal reading of the statute of limitations prevented the couple from filing their civil claims after 1998.

“It would have been impossible for them to bring a lawsuit at that time. Had the Rasmussens gone into court in the ’90s and sued the LAPD, LAPD would have come forward and said, ‘We’re just trying to solve this murder,’” said the family’s attorney, John Taylor.

Taylor continued, “The event that started the clock running to file a lawsuit was Stephanie Lazarus’ arrest. LAPD promised them they would answer. The family simply asked them to keep the promise and get them some answers.”

A jury convicted Lazarus of first-degree murder in 2012. She was sentenced to 26 years to life in prison.

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