Police are considering "an ongoing neighbor dispute over parking" as a possible motive for the Chapel Hill shooting that left three young Muslims dead on Tuesday, but they are still not ruling out a hate crime. Deah Shaddy Barakat, Yusor Mohammad and Razan Mohammad Abu-Salha were all shot in the head, according to CNN affiliate, WRAL.

The 46-year-old suspect, Craig Stephen Hicks, turned himself in on Tuesday night and is being held without bond in the Durham County jail. Police have said that Hick's is cooperating.

(To catch up on the Chapel Hill shooting, see HNGN's coverage of the incident from the beginning).

"Our investigators are exploring what could have motivated Mr. Hicks to commit such a senseless and tragic act," Chapel Hill Police Chief Chris Blue told WRAL. "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."

According to CNN, The Council on American-Islamic Relations asked police to "address speculation about a possible bias motive," and the Muslim Public Affairs Council is calling for a federal investigation "if the motives of the shooter are confirmed based on his previous social media posts."

Family spokeswoman Linda Sarsour told CNN that the victims had been threatened by Hicks before. Hick's wife released a statement on Wednesday expressing her shock by the shootings. "I can say that it is my absolute belief that this incident had nothing to do with religion or the victim's faith, but in fact was related to long-standing parking disputes my husband had with various neighbors regardless of their race, religion or creed," she said, according to the News & Observer in Raleigh.

The father of the two slain sisters doesn't believe that. "It was execution style, a bullet in every head," Mohammad Abu-Salha told the News & Observer. "This was not a dispute over a parking space; this was a hate crime. This man had picked on my daughter and her husband a couple of times before, and he talked with them with his gun in his belt. And they were uncomfortable with him, but they did not know he would go this far."

Posts from what is reportedly Hicks' Facebook page have been shared from a photo of his loaded gun, to a post defending LGBT rights, his defense of freedom of speech to a cover photo promoting anti-theism. On June 18, 2012, Hicks wrote, "Just so you know, while I am an outspoken atheist(obviously), I would never take away a persons right to religion."

According to CNN and other sources, Hicks wrote on his Facebook page, "When it comes to insults, your religion started this, not me. If your religion kept its big mouth shut, so would I."

HNGN has not been able to authenticate the source or context of the quote.