Charudatta Deshpande, Tata Steel's 57-year-old former chief of Corporate Communications, was found hanging at his Vasai home on June 28. No suicide note was found.
His friends and former colleagues alleged that he had been harassed.
A case has been registered at Vasai police station and the police are already probing the matter.
"I have received orders from the Home Minister, following which a parallel investigation is being done by my team. I am personally looking into the case," Joint Police Commissioner (Crime) Himanshu Roy told PTI.
One of the crime branch teams today visited Vasai police station to meet the investigating officers there and collected the case documents, police said.
The crime branch is also going through the technical data such as phone calls and emails received by Deshpande, days before he ended his life.
"There were allegations that Deshpande committed suicide following harassment by the employees of Tata Steel, where he had worked. We will look into that angle. If required, a team would be sent to Jamshedpur for the purpose of probe," said another crime branch official.
A delegation of the Mumbai Press Club, that included senior journalists Kumar Ketkar, Ayaz Memon and Charles Assisi, had met Patil last night and demanded an inquiry into Deshpande's death.
The delegation said the case should not be closed as an 'accidental death' incident but must be probed deeply as there were "sufficient prima facie evidence that he had been threatened by various Tata Steel officials and had been kept under house arrest in the days prior to the incident".
A written letter was also handed over to the Minister.
The delegation also demanded that the investigation be moved out from Vasai police station to a more competent agency like the Detection of Crime Branch or the state Criminal Investigation Department.
Reacting to the public outcry and the journalists' demand, the Home Minister told the Press Club delegation that he had entrusted the investigation to Deputy Superintendent of Police (Thane-Rural) C Devraj under the supervision of Roy.
"The minister said the precise contours of the investigation would emerge in three or four days and he invited Press Club officials to monitor the progress," said a statement issued by the Press Club.
A parallel departmental inquiry has been ordered by Tata Group chairman Cyrus Mistry into the circumstances leading to Charu's death.