Bodies of three people were on Tuesday found in government staff quarters at Rikana, Jogoo Road.
The bodies were of a woman, her son and a man.
The woman and her son were last seen on Sunday.
Neighbours however said they saw the man on Monday when he sent for charcoal.
The bodies were discovered after the child’s school administration called his father - who does not live with him - to find out why he had missed school on Monday.
The father, on failing to reach the his son's mother on phone, went to the house but no one opened.
A police report from Buruburu police station said, "A woman, her child and boyfriend were murdered at Jogoo Road Government Quarters, opposite Shell petrol station/St. Stephens ACK Church. The woman was working at the Registrar of Persons office, Mathare."
The body of the woman and her son had decomposed, while that of the man hadn't.
The living room was found in disarray showing a possible struggle before the murders.
The husband has confirmed that the slain man is not his brother
The woman and the child were found lying on the floor in their bedroom while the man was found, hands tied, in the bathroom.