Kumar directed the Inspector General of Police, Special Branch, G S Gangwar to meet the family, which originally is from Bihar and to assist them in any way possible.
"I am deeply saddened over the incident which deserves condemnation in the strongest words," Kumar told reporters.
The state government would provide assistance needed to rehabilitate the family if they decides to relocate to their native place in Bihar, Kumar said.
The chief minister said that he sent a cheque for Rs one lakh for the family of the victim through the IG (Special Branch).
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Kumar said that the Director General of Police Abhayanand had spoken to his West Bengal counterpart to find out the details of the incident.
He said that he also directed Gangwar to meet police officers in Kolkata to find out details of the case and submit a report to the Bihar government.
A 16 year-old girl, the daughter of a taxi driver, was gang-raped in October last year in Kolkata and again when she was returning after lodging a police complaint.