Woman shot dead in scrap with homeless man living in her apt.

A homeless man temporarily living with a Queens woman fatally shot her Monday after a heated argument over finances just steps from their building, a witness and police said.

Sydney Lugo, 24, and Tariek Sykes, 34, got into the squabble on the street near 109th Ave. and 120th St. in South Ozone Park about 9:20 a.m., cops said. The one-bedroom apartment belonged to Lugo, who allowed Sykes to share the space.

Police do not believe the two were romantically involved.

“They were blaming each other for financial problems,” said a 24-year-old neighbor who gave his first name as Islay.

The neighbor told the Daily News the fractious pair lived on the third floor, and he watched the argument escalate from his fourth-floor window.

“He was saying, ‘I have all the money in the world and you’re treating me like I’m broke.’ He was bragging about having [food stamps],” Islay said. “He said, ‘You know what?’ He paused, and he just shot her.

“He ended the argument with a bullet. He shot her in the left arm.”

Islay said the victim “was in disbelief, in shock.”

“She said, almost incoherently, ‘I can’t believe you shot me,’ ” Islay recounted. “He turned himself in to police immediately. He said, ‘I have nothing else on me.’ He put up no resistance whatsoever.”

Medics rushed Lugo (photo) to Jamaica Hospital, but she could not be saved.

According to Islay, Lugo had previously angered neighbors by playing loud music in the building.

“She used to leave a boom box in the hallway with the music turned up, facing outward and just leave,” he claimed.

He added that Sykes “was never around very much at all.”

“He was really well put together for someone who is homeless,” Islay said. “He was a pretty calm dude other than this outburst. She was the explosive one.”

Sykes was quickly arrested and charged with murder and criminal possession of a weapon.

Both Sykes and Lugo have been arrested multiple times, police said.