His remark led to walkout by the opposition members from the Assembly protesting the Left Democratic Front (LDF) government's approach towards a 'sensitive' issue.
When the UDF sought to take up the issue as an adjournment motion, the House witnessed heated exchange of words between the ruling and opposition benches. However, the opposition later accepted Speaker P Sreeramakrishnan's suggestion to present the matter as a submission.
Replying to the submission, Vijayan said there was no laxity in the investigation.
"Why the case is not handed over to CBI now? Because, the police investigation is progressing on the right track. A petition seeking CBI inquiry is also pending in the High Court," he said.
The chief minister asserted that the government was not interfering in the ongoing probe and said a special investigation team, looking into the case, has the freedom to arraign anyone as accused on the basis of evidence.
Vijayan also termed as "baseless" the opposition's charge that the government was trying to sabotage the probe to protect former Ernakulam Rural SP A V George, who was facing allegations of lapses on his part.
As many as 11 police personnel, including George, were placed under suspension in connection with the incident, he said.
Sreejith, who was taken into custody in connection with the death of a 55-year-old man, died at a private hospital on April 9. His relatives had alleged that Sreejith had died after being tortured in custody.
The government had later given Rs 10 lakh as a financial assistance to the kin of the deceased and a job to his wife.
On the opposition's complaint that Sreejith's family members were "dissatisfied" with the ongoing proibe, Vijayan said what he had come to know was that they were "satisfied" with the steps taken by the government.
Congress' V D Satheesan, who took up the matter in the House, attacked the LDF government alleging that it had recently sought legal opinion from the Director General of Prosecution (DGP) not to make A V George an accused in the case.
Satheesan also alleged that George had acted under the instructions of some local ruling CPI(M) leaders.
Leader of the Opposition Ramesh Chennithala said they were totally dissatisfied with the chief minister's reply and staged a walkout.
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)