"Evidence and circumstances of both crimes show distinct correlations between the two," said Jeff Klapakis of the Santa Barbara County sheriff's department.
Meanwhile, a hospital official says a sixth postal worker shot by the former employee had been in critical condition, but has died.
The shooter, Jennifer Sanmarco, 44, had a long history of mental problems and bizarre behavior, officials said. She had been placed on a medical leave from her postal job for psychological problems.
The Santa Barbara News-Press reported that police were looking into the separate slaying of a 54-year-old woman who was found shot to death in her Goleta apartment. The victim was a former neighbor of Sanmarco who had known the shooter.
The Press-News said police found a 9mm shell casing next to the former neighbor's body. Sanmarco used a 9mm handgun at the mail-processing facility where she once worked.
The newspaper quoted the ex-neighbor's boyfriend, Edward Blomfield, as saying that Sanmarco was "insane."
Blomfield said the dead woman had a mostly friendly relationship with Sanmarco, but that the pair had sometimes quarreled because of Sanmarco's bizarre behavior, which included loud, late-night singing.
The former neighbor was identified by her brother as Beverly Graham, 54.
Les Graham said his sister had complained about a neighbor who "used to come out and rant and rave in front of her building." He said the family suspects that the neighbor and his sister's killer was Sanmarco.
Investigators would not discuss a motive for Monday night's postal attack. It was believed to be the nation's deadliest workplace shooting ever carried out by a woman.
Through interviews with authorities and people who knew Sanmarco, a picture emerged of a woman on an odyssey of increasingly bizarre behavior after losing her job.
"We weren't sure what she was going to do next," said Terri Gallegos, deputy clerk for the city of Milan, New Mexico, where Sanmarco applied for a business license in 2004 for a publication called "The Racist Press" that she said she planned to launch. Another time she said she wanted to register a cat food business.
During one meeting, Gallegos said, Sanmarco carried on a conversation with herself "like she was arguing with someone but there was no one there."