The accused, identified as Vikram Bhatia, was in an inebriated state when he allegedly committed the crime and has been arrested, DCP (Northwest) Vijay Singh said today.
It was not clear whether Bhatia was about to kill himself as well, as a note was found in which the accused had scribbled that he took the extreme step as "nobody had helped him", he said.
Bhatia has been booked under Section 302 (murder) of IPC, said police.
"Bodies of the victims, identified as Nitu and three-year-old Naveen, were sent for postmortem examination and later handed over to their relatives," said a police official.
The incident came to light when Nitu's brother came to visit her yesterday evening and nobody opened the door, which was locked from inside.
He informed the landlord and they broke open the door and found the three family members lying motionless, said police.
They informed the police and all three were rushed to a hospital, where Nitu and Naveen were declared brought dead and Bhatia was found to be excessively drunk.
"Initially, it appeared like a failed attempt of family suicide. But when Bhatia's statement was recorded today morning, he confessed to have killed his wife and child, but did not mention anything about committing suicide," said a senior official.
Bhatia is a Delhi-based architect and had moved to a new rented apartment at Keshavpuram around a month ago. He had set up his office at the new residence itself, said police.
During further investigation, it came to light that Bhatia was under heavy debt and had been asking for money from all his relatives and associates, including his in-laws.
Some of them had helped the accused for quite sometime but later gave up, for which he was reported to be very depressed lately, said police.
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