He was fully dressed when the police arrested him and two bags containing identification, cash and other items were found on the sofa.
But Chinese national Wang Zhijian, 45, denied yesterday that he was planning to flee the murder scene.
He is accused of killing his girlfriend, Madam Zhang Meng, 41; her 17-year-old daughter, Feng Jianyu; and their 36-year-old co-tenant, Madam Yang Jie.
The murders took place in a sixth-storey flat in Block 349, Yishun Street 11 between 11pm on Sept 18 and 12.49am on Sept 19, 2008.
One charge for attempting to murder Madam Yang's daughter, Grace (not her real name), who was 15 then, has been stood down.
Grace cannot be identified as she was a minor at the time of the offence.
Police officers responding to a report of a person jumping out of the block went door to door to establish which unit the person had fallen from.
They noticed fresh bloodstains on the padlock on the gate of the unit where the murders took place. Wang was arrested shortly after.
In the unit, the police found two bags - a duffel bag and a laptop bag - on the sofa.
They contained Wang's clothes, local and Chinese currency, his passport and Chinese identification card and a digital camera, among other things.
Another bag with a combination lock containing two mobile phone batteries and two mobile phone covers was found in Grace's bedroom.
Wang refuted the prosecution's assertions that he intended to flee the crime scene.
Speaking through an interpreter, Wang admitted the two bags on the sofa were his.
He added: "(The third bag) was also mine, but why was it on her bed? If I wanted to escape, I would also take it.
"I reiterate that I did not want to escape. I don't know why the two bags were on the sofa. I don't know why (the third bag) was on her bed.
"I'm unclear. I don't know what happened."
Wang, cross-examined by Deputy Senior State Counsel Mohamed Faizal Md Abdul Kadir for the fourth day yesterday, said the third bag was his "best" bag; hence, it would make more sense for him to flee with it, instead of the other two.
Wang said he did not remember packing the bags.
He added that his passport was always kept in a plastic bag in the laptop bag, which was kept in a cupboard in his room.