The accused, Deepak Kumar, was reportedly addicted to tobacco despite being diagnosed with tuberculosis.
He was also lately undergoing treatment for suspected schizophrenia, a police official said.
He lived with his elder brother, Anil Kumar, and sister, Neelam, at their single-storey residence in Mahavir Enclave locality near Dabri. It was Anil Kumar who reported the incident to the police this morning, the official added.
In his complaint to the police, Anil said that when he was at office yesterday night, he received a phone call from a neighbour, who would often keep an eye on Deepak and Neelam in his absence, around 8 PM.
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Anil rushed home and found the door locked from outside.
Meanwhile, another neighbour informed him that he had seen Deepak walking towards the Dabri flyover. Anil went there on his motorbike and found Deepak sitting under a flyover.
"When he asked Deepak about their sister, he claimed to have no knowledge. He persuaded Deepak to sit on the bike and headed for home. After reaching home, Anil could sense some change in Deepak's behaviour. He kept on mumbling words, suggesting violence in connection with Neelam, and unclear sentences about him leaving the house soon," an official said.
Meanwhile, he also found out that Neelam had left her mobile phone at home. After about an hour, Anil assumed that Neelam must have gone to a relatives' house, where she often used to go after fights with Deepak, and went to sleep Anil woke up around 4 AM to check whether Neelam had come.
He also found that Deepak was not there on his bed.
He looked everywhere in the house and later headed for the terrace, where he found Deepak hanging from a beam near the staircase. He raised an alarm and neighbours helped him get the body down.
Later, Anil returned home to fetch money for Deepak's cremation and when he reached for a secret cabin in the bed box, he saw part of a stole hanging out.
He pulled out the box immediately and found Neelam's body with the stole wrapped around her neck.
He called up the police again and reported the matter, the police official said.
After preliminary investigation, it emerged that Deepak allegedly strangulated Neelam to death with the stole after a heated argument over chewing tobacco.
Neelam often used to stop her brother from consuming tobacco, especially after he was diagnosed with tuberculosis, and this led to frequent arguments - which many a times turned violent - between the two, the official said, adding, a case has been registered under relevant sections of IPC.