"I am saddened and worried.... If there is an attack on a journalist, it's an attack on me and that's how I am looking at the case," Kumar told reporters here.
Rajdeo Ranjan, Siwan bureau chief of a Hindi daily, was shot dead in a market place in Siwan. The journalist's family and opposition BJP have demanded a CBI inquiry into it.
"We have learnt that the victim's family wants a CBI inquiry. We are taking a decision to hand over the investigation to the CBI and it will be conveyed to the Centre," Kumar said.
Kumar said he had full faith in the state police which was conducting its probe in a free and fair manner but "circumstances have been created" where the family was in favour of a CBI inquiry.
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Asked about Opposition BJP's allegation that 'jungle raj' had returned in Bihar, the Chief Minister said it was a "baseless" claim.
"There is no reason for it. People who campaigned using 'jungle raj' term were defeated and cannot reconcile themselves now. They see everything from that prism."
"Bihar has been ruled as per law and it will be ruled by law. No one should have any doubt," he said.
Taking on the BJP, he said, "You look at it on case-to-case basis. Look at the Bihar government's response. You please compare our response to the response of BJP ruled states.
"But if you have already decided on a slant, I can't do anything. I can only work without bias."
"You look at the kind of atmosphere we have created in Bihar. But people will say what they have to say," Kumar said.