A case of murder was registered on a statement by the deceased's daughter at the RK Puram police station, a senior police official said.
The complainant told the police that the relationship between her father and mother was not cordial as he suspected her character, he said.
She said that her brother and his wife, who lived with them, had gone to attend a function in Burari on December 10, the official said.
She called her mother thrice the next day but her phone was switched off. She then spoke to her father who said that she had gone out, he said.
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The police was informed following which she was taken to a hospital where she was declared brought dead, the official said.
A crime team that visited the spot found that the floor of the dinning room of the house was washed, the official said.
The accused worked as a pump operator with the Central Public Works Department, he said.
He was arrested and a country-made pistol and two empty rounds were seized from him, the official said.