NEW YORK (AFP) - Investigators have failed to find a motive in one of America's deadliest mass school shootings, but said the shooter was mentally troubled and obsessed with the Columbine school shooting.

The official report into the Dec 14 massacre at Sandy Hook Elementary School closes the investigation, but does little more than shed new light on the extent of Adam Lanza's behavioural problems.

It does not make plain specifically what led him to murder 26 people in less than 11 minutes.

The deeply troubled 20-year-old first shot dead his mother in the head as she lay in bed then shot his way into the school he once attended in the sleepy town of Newtown in Connecticut.

Using a Bushmaster rifle he killed the principal and school psychologist, and injured two other staff members in the hall.

He then entered first grade classrooms eight and 10, killing two adults in each room, 15 children in classroom 8 and five in classroom 10 with the same rifle.

Police arrived less than four minutes after receiving an emergency call.

But Lanza killed himself a minute later with a single shot from a Glock 20, 10 mm pistol in classroom 10.

"In fewer than 11 minutes 20 first-grade pupils and six adults had lost their lives," said the report from the state attorney.

"The evidence clearly shows that the shooter planned his actions, including the taking of his own life, but there is no clear indication why he did so," the report said.

More than 300 live rounds were found at the school, a semi-automatic pistol on the shooter's body, a semi-automatic shotgun in his car and a rifle on the floor of his mother's bedroom.

All the firearms had been bought legally by Lanza's mother. A Christmas check for another rifle from his mother was also found during a search of their nearby home.

However, Lanza was known to have had "significant mental health issues" and was obsessed with mass murders, especially the 1999 shootings at Columbine High School in Colorado when two teenage boys killed 13 people, the report noted.