Prosecutors declined to immediately file a case against Russell Errett, 55, and asked for further investigation, according to Sarah Ardalani of the Los Angeles County District Attorney's Office.
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Errett was arrested Thursday in connection with the death of his wife, Hui Lui, 29, of Alhambra.
According to Alhambra police, Errett called 911 just after 1 a.m. Thursday to report the woman's fatal fall and said their 3-year-old daughter was in a car in the structure at the time. The child was not injured.
After questioning the 55-year-old, police said his story didn't match up, and they arrested him on suspicion of one count of murder.
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Investigators were looking into the possibility that the 29-year-old victim, Hui Li, was killed at a different location.
Investigators also said they believed the daughter may have witnessed the alleged killing.
According to the district attorney's office, charges could still be filed at a later date.
City News Service contributed to this report.