The 64-year-old Singh was stabbed multiple times and his throat had been slit, while his mother Gurcharan Kaur is suspected to have been strangled at their Phase-3 B2 residence two days ago.
Inspector-General of Police (Crime) Shashi Prabha Dwivedi, who heads the Special Investigating Team probing the double-murder case, said their investigation was progressing, but she refrained from giving any details.
"Our teams are working on scrutinising CCTV footages and call details in the case. Definitely there will be result in a day or two," Dwivedi said.
"We have been working on two-three theories, including property (dispute) angle and some relation in the case. We have zeroed in on certain suspects in this regard. Certain facts are being verified," said the official.
When contacted, SP (Detective) Harbir Singh Atwal said they have re-recorded the statements of a few close relatives of the victims this evening to double check some informations.
Singh and his mother were cremated yesterday.
A doctor said the victims seemed to have died between 2 am and 4 am on Saturday. The doctor said Singh was stabbed at least once close to his heart. "His throat was also slit."
The Punjab Police has set up an SIT to probe the crime.
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