The 20-year-old mum gave birth to her son weighing 5lbs 7oz on Monday – sparking widespread interest around the hospital.
But before anyone could catch a glimpse of the baby, the parents had discharged him and raced home.
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Dr Jaiprakash Narayan at Jawaharlal Nehru Medical College said: "A baby boy with two heads was born yesterday in a healthy state.
Two headed baby COVER ASIA PRESS
DECISION: Docs decided against operating on the baby boy
"The mother completed her pregnancy full term and was doing well post surgery but the baby suffered breathing issues."
After 32 hours, the baby sadly passed away, local reports say.
Dr Jaiprakash deliberated whether to operate on the small baby but eventually decided it was too difficult.
He added: "The operation is possible in some cases of conjoined twins but here it was nearly impossible.
"Despite having two pairs of all of their internal organs they were all trapped in one body, with only one pair of arms and legs. You cannot separate such children.