The woman, Tuntuni Choudhury of village Meherapur, claimed that she gave birth to a "boy" yesterday and the same was conveyed to her by the attending nurses.
The husband of the woman subsequently filed an FIR with the English Bazaar police station.
The child was being treated in the SNCU ward of the hospital.
Hospital authorities, however, maintained that the woman gave birth to a girl child and not as claimed by the parents.
Hospital authorities said, breathing trouble, low birth weight and infection were the prime causes behind the crib deaths.
Most babies were admitted to the hospital from Chanchol, Habibpur and Pakna areas of the district.