(CNN) -- A Las Vegas couple who gunned down two police officers and a civilian before killing themselves apparently looked at law enforcement as oppressors, a sheriff's department official said Monday.
Among the clues: a "Don't Tread on Me" flag and a Nazi swastika the couple placed on one of the police officers they ambushed Sunday at a pizza restaurant. They also pinned onto the officer's body a note saying something to the effect of "this is the beginning of the revolution," Second Assistant Sheriff Kevin McMahill told reporters.
"We believe that they equate government and law enforcement ... with Nazis," McMahill said. "In other words, they believe law enforcement is the oppressor."
Police said Monday that Jerad Miller shot Officer Igor Soldo in the back of the head, then shot fellow Officer Alyn Beck in the neck before Miller's wife, Amanda, pulled a gun from her purse and also fired on Beck.
They then ran to a nearby Walmart where they shot a bystander before barricading themselves inside the store during a brief firefight with responding officers.
Amanda Miller shot her husband repeatedly as officers closed in on them inside the Walmart, McMahill said. She then turned the gun on herself.
Investigators searched an apartment believed to be where the couple lived late Sunday night. They also are going through the couple's social media postings, McMahill said.
A woman who says she lived near the couple told CNN affiliate KTNV that the married couple liked to dress up as the villainous Batman characters Joker and Harley Quinn.
The neighbor, Krista Koch, told the station the man also sometimes dressed as Slenderman, a fictional horror character that recently surfaced in the stabbing of a 12-year-old girl in Wisconsin.
Ghoulish stabbing raises question: Who is Slenderman?
Koch also told the station the couple had told her they were going to carry out an attack, but she thought they were "crazy," so she dismissed what they said.
'Simply having lunch'
The pair began their attack about 11:20 a.m. Sunday, when they opened fire inside the restaurant where Beck, 41, and Soldo, 31, were having lunch.
"I just sat down to have lunch. The officers were sitting in front of me, at the table right next to me, and this man came in out of nowhere," a dazed Sheree Burns told KTNV.
"I thought he was going to get a drink, the way he walked up and walked past them. And then he turned around, pulled a gun on his right and shot the bald officer in front of me."
Sheriff Doug Gillespie said one officer was able to return fire.
"What precipitated this event, we do not know," he said. "My officers were simply having lunch."
The suspects took the officers' guns and ammunition, McMahill told reporters. They "made a statement -- something to the effect of, 'This is a revolution.' "
'That man was crazy'
As they walked out, they passed Alvaro Lopez.
"They had a backpack, and I saw a gun in their hand," Lopez told CNN affiliate KLAS. "He just told me to tell the cops that it was a revolution and that he'd just killed two cops inside CiCi's."
The pair ran to the Walmart and killed a shopper at the store's entrance, authorities said. Although a police representative had said that victim was female, a spokeswoman for the Clark County coroner's office identified the dead person Monday as Joseph Wilcox.
Wilcox "died attempting to protect others," Gillespie said.
Wilcox was armed with a concealed weapon and "heroically" tried to confront Jerad Miller after he fired his gun near the entrance, McMahill said. Wilcox passed Amanda Miller, apparently not noticing her, and Amanda Miller shot him, McMahill said.
Shoppers rushed toward the exit.
Pauline Pacheco saw the armed man and grabbed her father.
"We saw when the man was walking," she told KLAS. "He was shouting, yelling bad words, and suddenly he had a gun.
"It was terrible, it was terrible. That man was crazy."
Officers converged and exchanged fire with the couple, who ended the brief exchange in what McMahill referred to as a "suicide pact."
'Emptiness in our heart'
Beck and Soldo were both married with children: Beck left behind a wife and six children; Soldo, a wife and a baby.
A prayer vigil is planned Monday night, KTNV reported.
Meanwhile, Las Vegas police will be doubling up in patrol cars for at least the next few days as officers mourn the loss of two colleagues.
"We still have a community to police and we still have a community to protect," Gillespie said Sunday night. "We will be out there doing it with our heads held high but with an emptiness in our heart."