The gunman who rampaged through a Northern California community Tuesday, killing four people and wounding several others as he fired at an elementary school and apparently random strangers, had killed his wife the night before, according to authorities.

After fatally shooting his wife, Kevin Neal hid her body in their home and, hours later, embarked upon a bloody shooting spree through the rural region, targeting anybody he encountered along the way, Phil Johnston, an assistant sheriff in Tehama County, said Wednesday at a briefing.

Johnston said that before law enforcement officers killed Neal, the gunman wounded several children, striking one of the students at Rancho Tehama Elementary School during his rampage.

Chillingly, Johnston said the attack "could have been so much worse" because the gunman had apparently sought to enter the school while it was filled with children.

Neal, wielding a semiautomatic rifle and wearing a vest holding extra ammunition, had rammed the school's fence and tried to enter the building early Tuesday morning. However, because school officials had heard gunfire that morning, they hurried children and teachers inside and locked the school down, which kept the gunman outside, Johnston said.

"It is monumental that that school went on lockdown," Johnston said Wednesday. "I truly believe we would have had a horrific bloodbath in that school if that school hadn't taken the action that it did."

The gunman spent six minutes firing at the school, shooting out windows and spraying children with glass and hitting at least one child with a round, Johnston said. But when he could not get inside, he appeared frustrated and moved on, Johnston said.

Johnston said Neal had shot his wife sometime late Monday, cut a hole in his floor and hid her body there.

When police showed up Tuesday and spoke to neighbors, they reported thinking "there was a domestic violence incident" involving the couple Monday, though that had not been called in to authorities, Johnston said. He added that such incidents were "a very common thing with this couple," though he did not elaborate.

The gunman, who was officially identified Wednesday as local resident Kevin Neal, fired at cars and vehicles as he passed them. He was ultimately killed when law enforcement officers rammed his car and exchanged fire with him, fatally wounding him about 25 minutes after the first 911 call came in.

Neal's family had tried for years to get him treatment for his apparent mental illness, his sister, Sheridan Orr, said in a telephone interview.

The tragedy of the past two days had always been Orr's worst fear.

"If you could've seen him in those rages," said Orr, 46. "Anything was possible."

Neal's behavior escalated from a bad temper as a teenager to something more uncontrollable as he got older, Orr said. When he would call the family in a rage, upset over something, they would tell him to go to a mental health facility and that he needed medication. He would always refuse and he never received an official diagnosis, Orr said.

"He never should have had guns, and he should've been able to get mental health care," Orr said.

Their mother would break down and tell Orr that she didn't know what else to do or how to help her son, whom she talked to every day, Orr recalled.

"Her life's work has been to try to get Kevin some help and to find a way for him to be happy," Orr said. "He had a very erratic and uncontrollable temper that made it difficult to deal with him, and so it fragmented and fractured our family for many years."

She had not seen her brother in a decade and last spoke with him months ago. But when they were together, she said, it was horrifying to watch him spiral out of control. Something as simple as using the washing machine while he was trying to sleep could set him off.

What happened leading up to the bloodshed Monday and Tuesday remained unclear a day after the attack, Johnston said.

"I really don't know what his motive was," Johnston said. "I think he was just on a rampage, I think he had a desire to kill as many people as he could."