The police filed its application before Metropolitan Magistrate Sunil Kumar Sharma who fixed it for consideration on May 20.
In the plea, police has urged the court to initiate proceedings of polygraph test on Shashi Tharoor's domestic help Narain Singh, driver Bajrangi and friend Sanjay Dewan, saying they were hiding material facts relating to the case.
During investigations, several persons including Narain, Bajrangi and Dewan were examined as they were closely associated with Tharoor and Pushkar, and were also present at Hotel Leela Palace here just before her death.
It said that on January 17, Tharoor's close friend Sanjay Dewan came to the hotel at 5 pm and remained there till the discovery of Pushkar's death. He could not give plausible reason for cancelling his trip to Mumbai and his coming to the hotel in Delhi, it said.
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It alleged that Dewan did not give proper explanation for sending driver Bajrangi to bring Dr Mohan even without meeting Pushkar in her room.
Police said that Dewan did not produce his cell phone which was required to retrieve the text messages exchanged between him and Tharoor as per the call details. "It shows that he is hiding the material facts related to this case," it said.