A man hacked his wife and a three-month-old baby before turning the machete on himself, but did not die.
Daniel Sebuhoro, 36, is said to have a mental problem.
The cold blood murder happened in Rurambi village, Nyamirama sector in Kayonza district, on Wednesday.
Police said they are looking for more clues on the motive of the homicide.
“It is a tragedy. It appears the man had been having unusual behaviour. We have sent him to doctors for further check-ups since there are claims that he had a mental problem,” said the Police.
Senior Superintendent Benoit Nsengiyumva, Eastern Province police spokesman said a post mortem examination would be carried out, noting however that nobody else was thought to be involved in the murder.
“It appears he hacked his wife and child and then tried unsuccessfully to stab himself to death. Doctors will ascertain if he has a mental problem or not. He was clearly in a terrible state to have done such a thing,” he said.
According to Nsengiyumva, who is also the Regional Judicial Police officer in the Province, the crime attracts life imprisonment upon conviction.
“There is no short cut, murder according article 140 of the penal code is punishable by life imprisonment. But if the suspect is found to be insane, it may be a different story,” he said.
The incident stunned the local community, where the couple was known as a normal and happy pair.
Yesterday morning other neighbours, many of them in tears, gathered in the village to discuss the tragedy.
“We have only just found out and we are devastated. We all knew them as a happy couple. We don't know how this has happened. They were such a happy and friendly family,” said Jeanine Mukagatare, a neighbour.
“I can’t believe this has happened round here. It's a very quiet area, where everyone keeps busy with agricultural activities,” she said.