RICHMOND, Calif. - Three boys were booked yesterday for investigation of attempted murder in the beating of a month-old infant during the theft of a Big Wheel tricycle from a home in their neighborhood.

Authorities believe the boys, two 8-year-olds and one 6-year-old, broke into the home Monday evening while an 18-year-old stepsister was in another room.

They tipped over the baby's bassinet, then kicked, punched and possibly used a stick to beat the child, police said.

The infant was on life support with severe head injuries at Children's Hospital in Oakland, a spokeswoman said.

''Everybody's walking around here, going, 'I can't believe it,''' police spokesman Mike Walters said.

The stepsister, who said she heard nothing, found the baby lying motionless on a bed. The parents were out shopping with their two older children at the time of the robbery.

The names of the infant and the three suspects were not released.

Capt. Ray Howard said the suspects, neighborhood children known to the victim's family, are the youngest in memory to be investigated for such a serious crime. Besides attempted murder, they also were booked for investigation of burglary and conspiracy.

Detectives were baffled about a motive for the beating. ''Hard to reason why,'' Howard said.