Lazarus, 49, could be sentenced to death if convicted of Rasmussen's murder.
Rasmussen's father had urged police to investigate Lazarus, saying she had threatened his daughter in the months before her death, attorneys for the victim's family told the Los Angeles Times on Monday.
Neil Rasmussen urged in several interviews with detectives and in a letter sent two years after the killing to then-chief Daryl F. Gates that Lazarus be considered a suspect, but they were "dismissive" of his claims, said John C. Taylor, one of the family's attorneys.
The attorneys said Rasmussen is calling for an investigation of how the case was originally handled.
Lazarus, who joined the force in 1983 and since 2006 has worked with a unit tracking stolen art, was identified as a suspect through a recent DNA match of saliva taken from bite marks on Sherri Rasmussen's body, said Deputy Chief Charlie Beck.
Lazarus was being held without bail. She is charged with murder and using a handgun with the special circumstance of murder in commission of a burglary, which allows prosecutors to seek the death penalty.
Lazarus, who had already been an officer for two years, was not a suspect at the time of Rasmussen's death because detectives believed two robbers who had attacked another woman in the victim's Van Nuys neighborhood were to blame.
The case file mentioned Lazarus because she had once dated the victim's husband, John Ruetten, but investigators did not pursue her as a suspect until the recent DNA tests showed the attacker was a woman.
Beck said Lazarus' husband, Scott Young, who works as a detective in the San Fernando Valley, knew nothing about the slaying.
Beck refused to discuss further details of the case while investigators interview several sources: Ruetten in San Diego, detectives who first investigated the case who live in Idaho, and Lazarus' family in Arizona.
Detectives obtained a DNA sample from their colleague in late May and arrested her Friday at police headquarters.
Eric Rose, a spokesman for the Police Protective League, said he did not know if she had retained a lawyer, and her husband has not reached out for help.
Attempts to locate Lazarus' husband for comment were not immediately successful.
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