The 27-year-old committed the crime in Ol Kalou Constituency.
A resident told the Star that the man had intended to kill his wife and four-year-old son but that the woman fled while the child was in school.
He then went to his mother's house where he found his sister's daughter and cut her in the head with a panga. She died at the scene.
The killer then attacked his mother and left her unconscious before heading to school to pick his son.
At the school, head teachers asked if anything was wrong. He told them that he had killed his mother and niece.
"The teachers raised the alarm so he fled and jumped into a nearby dam. Residents found him trying to slit his throat and pulled him out," the resident said.
The area chief said the man's mother was taken to a nearby hospital and that she was unconscious. She suffered injuries to her head and other parts of the body.
Police took the suspect for treatment and the child's body to a mortuary in the area.
The killer's father said he returned home from Nairobi four days ago and told his wife that he intended to commit murder.
"He went to Nairobi a few months ago for work at construction sites. His wife informed me of what he said so I told her to stay alert," he said.
The father said he tried in vain to talk to his son to find out what the problem was.
"He could be under the influence of drugs. His acts could also be as a result of cult worship," he said.
Residents accused police of laxity, saying they took too long to report to the scene. They said that by the time officers arrived, they had disarmed the suspect and taken his mother to hospital.
-NDICHU WAINAINA