The bodies of K. Vijay Kumar, 57, and his wife Sita, 51, were found in two different rooms of their Kaka Nagar house Friday evening.
"The report suggested Sita first slit the throat of Kumar with a knife when he was sleeping and later hanged herself around 4 a.m. Friday," said sources.
Police said they have recovered the knife.
The sources added Sita was facing some mental problem for a few years and undergoing treatment at a private hospital. "The couple's relationship was strained for a while," said the officer.
Kumar was working as advisor (cost) in the ministry of food and civil supplies, while Sita was at a senior position at a bank.
The incident came to light when their 19-year-old daughter Waranya arrived at the two-bedroom house around 4.30 p.m. and called police when she got no reply after repeated knocks on the door.
The door was broken open, and Kumar was found lying in a pool of blood in the drawing room with deep wounds on his neck, while his wife was found hanging in a bedroom.
Joint Commissioner of Police Vivek Gogia had Friday said a case of murder had been registered since no suicide note was recovered and there was no sign of forced entry into the house with the door being found bolted from within.
"Neighbours said the family usually kept to themselves. The duo did not respond to the door Friday when a vegetable vendor knocked several times in the morning."
Waranya told police she had gone on a two-day trip to Rajasthan with her friends. Friday morning, she called her parents repeatedly but got no response.