(CNN) - Was it a dispute over a parking space or something more sinister that prompted the shooting death of three students in an apartment near the University of North Carolina at Chapel Hill campus?
Police said "an ongoing neighbor dispute over parking" might have been a factor in the shootings Tuesday evening but said they weren't dismissing the possibility of a hate crime.
The victims -- a newlywed couple and the bride's younger sister -- were shot in the head, sources told CNN affiliate WRAL.
Their families say the gunman had threatened the victims before, and they believe the shootings were a hate crime.
All three of the victims, Deah Barakat, 23, Yusor Abu-Salha, 21, and Razan Abu-Salha, 19, were Muslim. And given their religion and comments the alleged shooter apparently left on a Facebook page, many social media users wondered what role the victims' faith may have played.
The 46-year-old suspect, Craig Stephen Hicks, has been charged with murder.
At a news conference Wednesday afternoon, his wife said she was "shocked" by the killings and offered condolences to the victims' families.
"This incident had nothing to do with religion or the victims' faith, but in fact was related to the longstanding parking disputes that my husband had with the neighbors," Karen Hicks said.
Rob Maitland, her attorney, said the shooting "highlights the importance of access to mental health care services."
He declined to provide any details about the suspect's mental health history, but said, "obviously it's not within the range of normal behavior for someone to shoot three people over parking issues."
The father of the female victims, however, told CNN he was sure that wasn't true.
"We have no doubt that the way they looked and the way they believed had something to do with this," Mohammad Abu-Salha said.
When his son-in-law lived alone in the condominium complex, the family never had any problems. But once his daughter moved in, wearing a headscarf that clearly identified her as Muslim, trouble started, he said.
"My daughter, Yusor, honest to God, told us on more than two occasions that this man came knocking at the door and fighting about everything with a gun on his belt, more than twice," her father said. "She told us, 'Daddy, I think he hates us for who we are and how we look.'"
Learning from the police how his two daughters and son-in-law were killed has only made him more convinced.
"Now that we know from the police that they were shot in the head, very quickly, the three of them, one bullet each, in a very small space inside in the apartment. That's execution-style. I don't know, if that is not hate, what that would be."
Police: 'We will exhaust every lead'
The Council on American-Islamic Relations called for police to "address speculation about a possible bias motive," and the Muslim Public Affairs Council is requesting a federal investigation "if the motives of the shooter are confirmed based on his previous social media posts."
That's a possibility police are considering.
"Our investigators are exploring what could have motivated Mr. Hicks to commit such a senseless and tragic act," Chapel Hill Police Chief Chris Blue said. "We understand the concerns about the possibility that this was hate-motivated, and we will exhaust every lead to determine if that is the case."
Ripley Rand, the U.S. attorney for the Middle District of North Carolina, said Wednesday that there was no federal investigation underway, and the incident appeared to be isolated rather than part of an organized campaign against Muslims in the state.
Police are examining the suspect's computer to see if they find anything indicating bias against Muslims or any intent to carry out an Islamic or religious-bias attack, according to a law enforcement official briefed on the investigation.
So far, nothing has turned up to indicate a hate crime, the official said.
The FBI is assisting police, who are leading the investigation.
"The Chapel Hill Police Department has requested the assistance of the FBI to process evidence in a triple homicide investigation," the FBI said in a statement. "It is standard practice for our state and local law enforcement partners to enlist the expertise and resources of the FBI as needed."
Official: Dispute flared over parking space
According to the law enforcement official briefed on the investigation, Tuesday's altercation started after Hicks found a car belonging to one of the victims in what he claimed was his parking space. Then Hicks went to the victim's condo and shot all three people in a confrontation.
Hicks turned himself in to police Tuesday night and is being held in the Durham County Jail without bond. He is cooperating with investigators, police said Wednesday morning.
Hicks has no criminal record, the official said.
His wife told reporters he had been studying to become a paralegal.
He told police that he liked guns and visiting shooting ranges, but had stopped going because of the cost, the official said.
Focus on possible Facebook post
Word of the case spread rapidly on social media.
The hashtag #chapelhillshooting and #MuslimLivesMatter quickly topped Twitter's trending topic early Wednesday morning.
In one post widely shared online, Hicks, who claimed he is an atheist, allegedly wrote: "When it comes to insults, your religion started this, not me. If your religion kept its big mouth shut, so would I."
CNN couldn't independently confirm the authenticity of the post or his Facebook page.
Barakat was a second-year student at the UNC School of Dentistry. His wife had recently been accepted to study there next year. And her sister was a freshman studying architecture at North Carolina State University in Raleigh.
The condominium complex where they were killed is home to many university students. Tuesday night, friends and family members gathered, crying or comforting each other, as they waited for word from officers.
"It's been hours. Just tell me if he's alive," one man cried out.
An officer tried to calm him down. "Give us more time," he said.
At least 2,500 people joined a candlelight vigil in honor of the victims at the University of North Carolina at Chapel Hill Wednesday evening, a university spokesman said.
The shooting has left the community shaken, Chapel Hill Mayor Mark Kleinschmidt told CNN's "The Situation Room." Chapel Hill is a safe place for Muslims and people of all faiths, he said.
"We're all struggling to understand what could have motivated Mr. Hicks to commit this crime. ... It just baffles us," he said.