The baby, who is yet to be named, was born to factory worker Vinod Kumar and his wife Sushma three weeks ago in northern India and has been drawing a stream of curious observers and others who consider her a deity in this deeply religious Hindu-majority country.
"I had never seen something like this in my life so naturally I was a little scared when I first saw her," her father said at the weekend at the family's mud-and-brick house in Noida town, about 50 kilometres (30 miles) northeast of New Delhi.
The girl has found easy acceptance in Kumar's large, extended family, who say they have no plans to consult doctors to check if the girl can receive treatment or corrective surgery.
"The doctor said everything is normal when she was born. So where's the need to get medical help?" said the child's father.
"She's fed through one mouth and sucks her thumb with the other. We use whichever mouth is free to feed her," the 24-year-old Kumar said, adding she is eating and breathing normally.
Doctors said it was an extremely rare case, with the girl having two skulls joined together, and that separating them was out of the question.
Last Mod: 06 Nisan 2008, 19:38
"Since the heads are fused, separating them is not possible," paediatrician D.K Gupta of the All India Institute of Medical Sciences told the Hindustan Times newspaper on the weekend.
But doctors said the girl should be examined thoroughly to study the possibility of complications.
"Clearly the child is in no immediate danger but it has to be checked whether the oral and nasal cavity and other passages" are functioning properly, paediatrician Gupta said.
The case comes just months after Indian doctors performed a rare, marathon surgery to remove the extra limbs of a girl born with four arms and legs.
Two-year-old Lakshmi Tatma's case captivated the nation last year as domestic and international media focused on her complicated surgery performed in southern Bangalore city in November.
This year, Lakshmi started taking her first steps with the help of a baby walker, delighting her parents and doctors.
Lakshmi, named after the four-armed Hindu goddess of wealth, was born fused to the pelvis of a twin that had stopped developing in her mother's womb — a condition that occurs once in 50,000 conjoined twin births.
Kumar said he had heard about Lakshmi, but did not want to change anything about his daughter's features.
"Whatever God has given me is acceptable. What can we do about it?" he said, lifting the baby to take her away after allowing a brief glimpse of her as neighbours crowded around her cot.
"This child is very special to us," the baby's grandfather chimed in, gazing lovingly at the infant.