The interrogation led by Deputy Superintendent of Police Deepak Deoraj lasted for about nine hours.
The team comprised of officials from the Mumbai Crime Branch and Thane police, Deoraj said and hinted that they were likely to continue the interrogation tomorrow.
Maharashtra Home Minister R R Patil had ordered Mumbai Crime Branch chief Himanshu Roy to probe the alleged suicide of Deshpande (57) who was found hanging at his Vasai home on June 28.
A departmental inquiry into the circumstances leading to Deshpande's death has also been ordered by Tata Group chairman Cyrus Mistry.
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Meanwhile, Tata Steel said in a statement in Delhi that it has expanded the committee formed to ascertain the facts by inducting an independent director of the company.
"Further to our communication dated July 2, on the appointment of the committee to ascertain the facts relating to the allegations surrounding the demise of Charudatta Deshpande, the Board of Tata Steel has expanded the committee with the induction of O P Bhatt, independent director of the company," it said in the statement.
"Earlier today, a team of Maharashtra police officials investigating the demise of Charudatta Deshpande visited Tata Steel's offices in Jamshedpur. Tata Steel's officials have extended their full support and cooperation to the ongoing investigations," it said.