(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 pinned onto the other 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 don't necessarily believe that they are white supremacists or associated with the Nazi movement. We believe that they equate government and law enforcement ... with Nazis," McMahill said. "In other words, they believe that 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 and killed 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.
Police are still in the early stages of their investigation. At this point though, they believe the couple acted alone and that the officers shot were targeted at random.
Investigators searched an apartment late Sunday night that was believed to be where the couple lived. They were going through the couple's social media postings, McMahill said Monday.
Police also recovered hundreds of rounds of ammunition from the couple's backpacks at Walmart, suggesting they were prepared for a lengthy gun battle at some point, he added.
"There is no doubt that the suspects have some apparent ideology that's along the lines of militia and white supremacists," McMahill 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 CNN affiliate 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.' "
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 Walmart where Jerad Miller fired off one round and told people to get out, McMahill said.
A shopper, identified as Joseph Wilcox, told his friend he was going to confront the suspects.
"He was carrying a concealed weapon, and he immediately and heroically moved towards the position of Jerad Miller. Upon completing that action, he did not realize that Amanda Miller was with Jerad Miller," McMahill told reporters.
He continued: "As soon as he began to confront Jerad Miller with his firearm, Amanda Miller removed her firearm and shot him one time in the ribs area where he immediately collapsed."
Wilcox, 31, "died attempting to protect others," Gillespie said.
Shoppers rushed toward the exit. Officers converged and exchanged fire with the couple, holding the Millers to the rear of the store.
At one point, Jerad Miller built a defensive position around his wife. She was seated and appeared to be suffering from a gunshot wound, McMahill told reporters.
He then laid on his stomach in front of Amanda, who fired several rounds into her husband, killing him.
"At that point, Amanda took her handgun and ended her own life with one gunshot wound to the head," said McMahill, describing the deaths as the result of a "suicide pact."
'See something, say something'
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.
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.
McMahill told reporters he'd heard unconfirmed reports the suspects spoke to a neighbor about the attack before it happened.
"You know we have the 'see something, say something' campaign," he said, urging people to call police when something doesn't feel right.
"We need to hear about those times when individuals or groups of individuals are talking about going out and committing acts of violence -- whether it's against the police or anybody else in our community,"McMahill said.
"We need to hear from our citizens. They're the best eyes and ears that we have out there."
'Emptiness in our heart'
Beck and Soldo -- the two officers killed -- were both married with children: Beck left behind a wife and three 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."