The police say they are still trying to identify the woman.
The burnt body of a woman, tied to a cot, was found in a village in western Uttar Pradesh's Bijnor district on Friday. Three empty cartridges were also recovered from the spot, suggesting that she was also shot.
The body was discovered by villagers near a tubewell on the outskirts of the village last evening. The police say they are still trying to identify the woman.
"We are collecting DNA samples to ascertain her identity," said senior police officer Laxmi Niwas Mishra.
It is not clear if the woman was also sexual assaulted.
The police say they will try to identify the woman as soon as possible and make arrests in the case.
In another shocking incident, the dead body of a young woman, without clothes, was found near a forest in eastern Uttar Pradesh's Bahraich district. The woman's face had burn marks, seemingly from acid, to prevent identification.
The girl's face although burnt is recognizable, police said, adding that the woman appears to be from outside the village.
"The body of the 20-year-old woman was found with out clothes in a forest area in a village in Bahraich. There are burn injuries on her face. We are trying to identify her. As per our initial investigation the victim does not appear to be from the village," Additional SP Bahraich Police Ravindra Singh said.