"The incident took place at 5 pm yesterday. One Sajib Halder killed his parents and his cousin sister at his residence," officer-in-charge of Arundhatinagar police station, Rohul Alam told reporters.
The cousin used to stay with the Halder family.
The police visited the crime scene after neighbours informed them and found the man sitting beside the bodies.
The bodies were lying in a pool of blood, he said.
The police recovered a dumble and an iron rod from the spot, Alam said.
The man, who was reportedly mentally unsound, was arrested, Alam said.
The deceased were identified as Babul Halder (59), his wife Sabitri (52) and Shibu (32).