At least eight people were sued for hurling acid on three members of a family in Gopalpur village under Kushtia Sadar upazila.
Ayub Ali, father of college girl Sonia Khatun, filed a case with Islami University police station Monday morning.
Shariful Islam, officer-in-charge of Islamic University police station, told the Dhaka Tribune that they had started drive to arrest the culprits.
Three people suffered severe burn injuries on Saturday as some miscreants hurled acid on them while they were asleep at their residence.
The victims of the gruesome attack are Saleha, 60, and her two children Sonia Khatun, 18, and Titumir. They were admitted to Kushtia General Hospital in critical conditions.
Quoting family members police said some unidentified culprits had thrown acid on the trio through a window around 10:30pm while they were asleep and had then fled the scene immediately.
Hearing their hue and cries, their neighbouring people rushed to the spot and took them to the hospital.
Dr Amio Kumar, medical officer of Kushtia General Hospital, said they had referred Sonia, who is a student of a local college, to Dhaka for better treatment as her burns were comparatively worse than the others.
Police visited the spot and arrested Nayeb Ali for his alleged involvement with the incident.