Police said they are also probing whether there were other reasons behind her killing.
In a suspected case of honour killing, the West Bengal Police has arrested the father and brother of a Muslim woman on the charge of murdering her for being in a relationship with a Hindu man.
The duo, residents of Bihar's Jamalpur, were arrested from Kolkata on Monday by Purba Burdwan district police, a senior officer said.
Police had on August 31 recovered the body of a woman whose face was mutilated with a stone, from an agricultural land around 19 km from here, he said.
"During the post-mortem, we found two numbers jotted on her body, following which we got hold of the man with whom she was in a relationship," the officer said.
A police team then reached the man's residence in Mumbai, and he gave details about the woman's place of residence and her family members.
Acting on his inputs, police arrested the woman's father and brother, who worked as drivers in Kolkata.
The two admitted to killing the woman with a rope inside a moving vehicle, while they were taking her back to Jamalpur and then dumped her body in the agricultural land after defacing her face with a stone, the officer said.
Police is also probing whether there were other reasons behind her killing, he said.