The police said it was looking into the allegation.
The baby boy, born to Saraswati Naskar, was stolen from Calcutta Medical College and Hospital this afternoon by a woman who said she was taking him away for vaccination, the family alleged.
"A woman came to me and asked if I had any family member around. Upon learning that there was none, she said she needs to take my baby for vaccination and left," the mother alleged.
The mother said that she searched for her baby but he was nowhere to be seen. Even the security guards couldn't help her.
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Further footage from a CCTV installed at the CR Avenue metro station showed the same woman along with the baby boarding a Garia-bound metro.
"We are looking out for the woman with the baby. Photos grabbed from the CCTV footage have been circulated to all local police stations and security personnel at every entry and exit points of the city," a senior officer of the Kolkata Police said.
Family members of the baby have lodged a complaint at the Bowbazar Police station in connection with the incident.