Women and Social Welfare minister Sabitri Mitra, who proposed the idea at a meeting of the state women's commission on Thursday, also said that a bell would be placed near the cradles or drop boxes which would be rung by those leaving behind babies to alert the authorities.
The state run hospitals would take care of the abandoned babies, she said, and send them to adoption centres.
Ms Mitra hoped that the measure if implemented would prevent illegal adoption rackets.
The idea, she said, has been placed before the Child Welfare minister Shyamapada Mukherjee.
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