Police said the identity of the man is yet to be confirmed.
As per the preliminary investigation, the two began to live together recently. Last night they had a fight and the man locked the house and cut his neck himself, a police officer said.
"The woman claimed that she had tried to call for help but none could hear her because the house was locked and she could not find the key. She also claimed that she tried to stem the bleeding by putting some tapes on the man's wound.
The local police were informed by the neighbours this morning and took the man to a nearby hospital, where he was declared dead, he added.
Forensic experts and homicide detectives of the Kolkata Police have collected clues from the premises and the body has been sent for post mortem, the officer said.
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