Moumita's husband has been detained for questioning.
A young law student was found dead in a pool of blood with bullet injuries on an expressway in Bengal's Nadia district, around 115 km from Kolkata, on Friday night.
21-year-old Moumita Biswas was found after locals alerted the police about a body near a water supply project on the expressway. She was taken to a hospital where she was declared dead.
Her estranged husband has been detained for questioning.
Police suspect that she was murdered shortly before midnight. The body has been sent for post mortem and a case has been registered by the police.
Moumita, a resident of Khardah, is the daughter of a police constable.
Her father Biman Biswas said that she was missing since last Friday.
"Prima facie we suspect this could be a fall out of a romantic relationship but nothing has been established so far," police officer Kostabaditya Acharya told reporters.
The woman got married last year but had been living separately since March. Her in-laws said they were not in touch with her.