Tien Hua, 33, was hit three times, including once in the head, according to a source familiar with the investigation but not authorized to make a statement.
SWAT officers who entered the barricaded home had been informed that Hua, a suspect in the slaying of a 27-year-old Hollywood Hills man, may have been armed with a handgun. But no firearm was recovered at the scene, according to the source.
LAPD officials would not describe the object in Hua's hand.
The fatal shooting marks the 21st time LAPD officers have killed an individual in 2015. The shooting is under investigation by the LAPD, the inspector general and Los Angeles County district attorney's office, which is standard practice in all LAPD uses of deadly force.
LAPD detectives tracked the suspect to the home in the 3500 block of Strang Avenue and were attempting to serve search and arrest warrants when the standoff began, according to Officer Mike Lopez.
About 8 p.m. Tuesday, SWAT officers fired teargas into the home to drive out the man. The officers entered the house and discovered that Hua had escaped into the backyard, where he was confronted on a shed rooftop.
Hua was a suspect in the slaying of Henry Estrada, who was gunned down Sunday morning in the 2000 block of Sycamore Avenue in the Hollywood Hills. LAPD officers responding to reports of gunfire found Estrada, who died at the scene. The gunman chased Estrada up a hill and shot several times, police said.
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