Investigators spent hours at the Hollywood apartment building in the 6200 block of De Longpre Avenue where the victim, 66-year-old Hervey Medellin, lived.
Neighbors said they have been interviewed by investigators asking questions about Medellin and a younger man he lived with on the third floor.
Detectives were seen carrying out bundles of potential evidence.
Authorities said they believe Medellin was murdered and his body parts were then dumped at Bronson Canyon Park.
Bronson Canyon Park reopened Friday morning. It had been closed since Tuesday, when two women walking dogs found Medellin's severed head inside a plastic bag. His hands and feet were discovered about 50 yards away the next day.
The medical examiner's office was able to use fingerprints from the victim's severed hand to identify him.
"He was just a sweet, quiet old man with a dog," said neighbor Genevieve Fahey.
Anyone with information related to the case is asked to call the Los Angeles Police Department Robbery-Homicide Division at (213) 486-6890.