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Jagat Singh is the son of senior Congress leader K Natwar Singh and a general secretary of the Indian Youth Congress.
He was questioned about his relations with his wife and his whereabouts at the time of her death, police sources said.
Jagat Singh is believed to have told the police that he was at a party at that time, sources said.
Police are now cross-checking this and other details given by Jagat Singh, they said.
Singh and Natasha had been living separately for over two years and Natasha had even filed for divorce.
Police also recorded the statements of Natasha's relatives and friends, particularly those who had received SMS messages from the deceased's mobile phone.
While police have registered a case of murder, they are saying that suicide could not be ruled out.
EARLIER REPORT: Probe picking up momentum: Cops
More reports on Natasha Singh's death
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