Policeman Iskandar Rahmat was the investigating officer when businessman Tan Boon Sin made a report about theft at Bedok police station in November last year.
But he was later taken off the case, said a police press conference.
The case was passed on to another officer who was already investigating a series of similar thefts.
Iskandar, 34, a senior staff sergeant, was arrested on Friday for the murder of Mr Tan, 67, and his son, Mr Tan Chee Heong, 42.
Beyond that encounter, it is unclear the extent Iskandar is related to the victims.
The elder Mr Tan, who owned a car workshop in Kaki Bukit, was killed in his Hillside Drive terrace house in Upper Serangoon on Wednesday afternoon.
His son was seen staggering out of the house before collapsing in a pool of blood. Minutes later, someone drove the elder Mr Tan's Toyota Camry out of the house. It ran over the younger Mr Tan and dragged his body for 1km.
Police said Iskandar, a cop for 14 years, fled to Malaysia that night on a scooter. He was arrested in a Johor restaurant at 11.30pm on Friday.
The police conference, chaired by Deputy Prime Minister and Home Affairs Minister Teo Chee Hean and Police Commissioner Ng Joo Hee, has ended.