The child was rescued by co-passengers and admitted to Naihati State General Hospital.
The woman, Purnima Saha of Kalyani, had boarded the up Krishnagar Nagar suburban train from Naihati when the child landed on the tracks after being flung by her.
Superintendent of Railway police, Sealdah, Utpal Naskar said the woman was being interrogated.
The woman, who was travelling with the baby, is the mother of another 14-year-old daughter. Her husband who was on a visit to Tarapith, sells lottery tickets.
Naihati GRP sources said the woman was mentally unstable.
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