A forklift-driver was charged on Friday with the murder of Ms Jasvinder Kaur, 33, whose decapitated body was found floating in Whampoa River on Dec 12.
The accused was identified in court as 25-year-old Gursharan Singh, who police had previously said was a friend of Ms Kaur's husband Harvinder Singh. All three are Indian nationals.
Gursharan Singh is accused of causing the death of Ms Kaur at a residence in Balestier Road, together with an "unknown male person" between Dec 10 and Dec 12.
The police on Thursday had also said that they are now looking for Mr Harvinder Singh to help in their investigations. The husband had left Singapore 30 minutes before Ms Kaur's body was found - without her head and hands - and reported to the police by a jogger and cleaner at about 7.30am last week. The senior logistics coordinator left by bus through Woodlands Checkpoint, but it is not known if he is in Malaysia.
Police, however, said they have "sought the assistance of our counterparts in the neighbouring countries to trace his whereabouts".
The couple were living in Balestier and neighbours told the police that there was no sign of any quarrel between husband and wife before her death.
Ms Kaur's body was wrapped in a trash bag when it was found floating in the waterway between McNair Road and St George's Road. Besides her missing head and hands, her arms had been apparently mutilated.
About 30 police officers spent three hours searching through five tonnes of rubbish at Tuas South incineration plant and have yet to find her body parts.
The police said the Indian High Commission is helping to contact the family of Ms Kaur, who is a beautician.
The accused was arrested on Wednesday at his workplace, a warehouse in Sims Avenue. When The Straits Times visited the warehouse on Thursday night, a staff member said his boss is not in Singapore and may not be aware of the arrest.
He added that the forklift driver is not a permanent employee and had joined the company recently. Gursharan Singh had come to Singapore to work as a construction worker in September 2010, but he held a Special Pass when he was arrested.
Anyone with information on Mr Harvinder Singh may call the police on 1800-255-0000 or give information online at www.spf.gov.sg/CrimeStopper