MECHANICSVILLE, Va. — A suburban Richmond man going through a custody battle with his estranged wife used duct work to channel the exhaust from a van into a bedroom, where he sliced his neck and those of his twin 3-year-old daughters, authorities said Monday.

Hanover County deputies received a call just after 3:30 p.m. Saturday from the girls' mother, Kristina Hooper. When they arrived, she was crying on her knees at the end of the gravel driveway, court records said.

"My babies are dead, they're in the house," she told deputies, according to a search warrant affidavit returned Monday.

The Hanover County Sheriff's Office said the exhaust delivered a lethal amount of carbon monoxide into the home. It said 40-year-old Robert D. King and twins Caroline and Madison King died as a result of either the exhaust or a combination of that and the cuts on their necks.

Deputies were overcome by fumes and had to ventilate the one-story brick ranch home before entering.

Flexible tubing was attached from the exhaust pipe of the vehicle and snaked into the front bedroom, where the three were found dead. Authorities removed duct work, two notes, a video camera and several other items from the home.

The twins lived with Hooper at another Hanover County address, but both parents were fighting for custody, documents said. It did not say in the documents why the girls were with their father that day.

Hooper's attorney's office declined to comment. A number for the mother was no longer in service.

King filed for divorce in October, accusing Hooper of abandoning the family a month earlier. The two were married in March 2008, and the girls were born that August.

Hooper countered that King's paranoid behavior and verbal abuse, combined with a "significant shoplifting problem," were the cause of the failing marriage — something he denied. She claimed she didn't abandon the family, but that both agreed despite marriage counseling that the relationship was doomed.

In court documents, Hooper said the separation followed a decline in King's mental state "which created living conditions which were intolerable and constituted constructive desertion and cruelty."

King's divorce attorney did not immediately return a message seeking comment.

On Sunday, mourners placed flowers on the front porch of the home where the bodies were found.

"It's a tragedy all the way around, to lose two little girls at such a tender age," a neighbor, Jean Atkins, told the Richmond Times-Dispatch. "It hurts. It hurts everybody that has heard the story."

Associated Press writer Steve Szkotak in Richmond contributed to this report.