Sources in the Central Bureau of Investigation said that he was asked several questions related to Sheena's murder, his conversations with his wife Indrani Mukerjea and his own statements by officials at the Central Forensic Science Laboratory.
Sources added that some answers given by him indicated "deception".
The agency will have to produce him before a special court in Mumbai on Monday.
CBI sources said Mr Mukerjea was questioned in Delhi yesterday for nearly six hours with the questioning focused on whether funds allegedly siphoned off from the media house founded by him and Indrani Mukerjea were parked in an overseas account of Sheena Bora resulted in a dispute between Indrani and her daughter.
They said the agency confronted Peter Mukerjea with the Income Tax returns filed by him and Indrani to ascertain their various investments in India and abroad.
The sources claimed that on many accounts his answers were purportedly not convincing and changing which prompted CBI to put him to polygraph test.
Sheena Bora, Indrani's daughter from an earlier marriage, was allegedly killed by her mother, her former husband Sanjeev Khanna and her former driver Shyamvar Rai in April 2012.
While seeking custody of Peter Mukerjea from Mumbai special court, the CBI claimed on November 26 that he has told the agency that accounts might have been opened in the name of Sheena by Indrani Mukerjea in banks in Hong Kong and Singapore.
According to the CBI, the couple's company 9X Media Pvt Ltd carried out its internal audit in which nine companies having shareholding as on March 2009 were found to have instances of misallocation and siphoning of substantial amounts of funds by Peter and Indrani Mukerjea.
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