The body of the woman was found in naked state and therefore foul play cannot be ruled out, the police said.
The incident happened under the jurisdiction of Harehunj police station.
The deceased were identified as Kritu Bhuiyan (40) and his wife Mala Devi (30).
It appeared that the couple was killed yesterday night with a sharp weapon, a police officer said.
The couple used to run a food stall in the village. The villagers suspected something wrong as the couple did not open the stall today morning and found the bodies when they went to the couple's house to find out what happened, the officer said.
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Sanoj Choudhary, the officer-in-charge of Harehunj police station along with Harehunj BDO Shravan Ram reached the spot and handed over Rs 20,000 to the deceased couple's relatives.
They also assured the villagers that the couple's children - two daughters and a son, all of them minors, would be enrolled in good schools.
They assured to provide all other benefits as per governments norm.
Later, Choudhary said prima facie, it seemed to be a case of rape and murder.
An investigation has been initiated, he added.