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The Chief Minister also promised a job to one of her family members and said the state government will bear the legal expenses the family would have otherwise incurred.
Mita, wife of Rana Mondal of Kushberia near Kolkata, allegedly committed suicide on Monday after a spat with her husband. But her family claimed she was killed by her husband and in-laws.
Police have arrested Mita's husband Rana and his father Bijendra Mondal but his mother and brother are absconding.
"It is a very sad incident. We will make sure that the offenders are punished," Banerjee said after meeting Mita's family at the state Secretariat Nabanna.
Banerjee will give Rs 65,000 from the Chief Minister's Relief Fund to enable her family to repay their debts.
"The family has fought hard to come out of poverty. We will donate the amount they borrowed for their daughter's (Mita's) marriage and also provide a job to one of the family members," she said.
Hours before Banerjee's media conference, Chief Secretary Basudeb Banerjee made public Chief Minister's order for a probe by the CID of West Bengal Police .
"The government is keeping a close watch on the case," the top bureaucrat told the media.
Mita's batch mates from Jadavpur University have started an online campaign following her death. The students have also organised a rally from Jadavpur University to Dhakuria in south Kolkata for demanding justice to Mita.
"It is a clear case of murder, not suicide. Her head was bruised and nose was bleeding. There were several wounds all over her body. Moreover, the room she used to live in does not have the set-up which she could have used to hang herself," Mita's bother said.
"Her husband Rana told us Mita had attempted suicide and a suicide note was found. But police did not find any such note," he added.
Mita's family alleged her husband was an alcoholic and often beat her up.
"Mita confided in her father that her husband had asked for Rs 1 lakh. She asked for the money from her mother during her last visit to her parental house," said a relative.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)