The court's order came after the three suspects -- Shashi Tharoor's domestic help Narain Singh, driver Bajrangi and friend Sanjay Dewan -- said they were willing to undergo the polygraph test.
"Application for polygraph test on the three suspects is allowed, subject to NHRC and the Supreme Court guidelines," Metropolitan Magistrate Sunil Kumar Sharma said.
During the hearing, the police told the court that these three persons were examined during the investigation but they are hiding some crucial facts.
"They are not disclosing all the facts. They are hiding some crucial facts regarding the injuries on Sunanda Pushkar's body," the police claimed.
The counsel appearing for the three suspects told the court that their clients have fully cooperated with the police.
"The Supreme Court has said that this (polygraph test) is not a relied upon evidence but if the police wants to do this, we are giving the consent," the counsel said.
The counsel also told the magistrate that police should inform the court regarding the questions which they want to ask during the test.
"My clients are ready to undergo the polygraph test because we don't want to give the impression that we are running away from the probe," the counsel said.
The police, in its plea, had urged the court to initiate proceedings of polygraph test on the three suspects saying they were hiding material facts relating to the case.
Police had said that during investigation, 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 just before her death.
"During investigation, it has been found that the three persons are concealing material facts and did not disclose several issues related to the death of Sunanda Pushkar," the plea filed by SHO of Sarojini Nagar Police Station had said.
The police had said in the plea that on January 17, 2014 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 had said.
"He remained silent about the power cut on January 17, 2014 at about 7 pm in room no. 345 at Leela Hotel just before the discovery of the death of Sunanda Pushkar, while he was very much present in the room along with Shashi Tharoor," the application had said, adding that he did not properly reply to questions regarding the injuries on Pushkar's body.
The police had claimed he did not wake up Pushkar for two and a half hours and also not explained why he preferred Dr Rajan Mohan, who came all the way from Patel Nagar in West Delhi, over the hotel doctor who could come immediately.
It had alleged that Dewan did not give proper explanation for sending driver Bajrangi to bring Dr Mohan even without meeting Pushkar in her room.
Police had 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 had said.
Regarding suspect Narain, police ahd claimed it was found that he had accompanied the Tharoor couple from KIMS Hospital in Thiruvananthapuram, and remained with Pushkar in the hotel from January 15-17, 2014 till her death and that he was very well-acquainted with the facts relating to her death.
"But he did not disclose how the injury marks had taken place on her body and relations between Tharoor and Pakistani journalist Mehr Tarar which was a bone of discord between the couple", the plea had said.
It had added that Narain cited the reason for Pushkar's stay in the hotel to be the ongoing repair work at their residence in Lodhi Estate but it was found that the work was over before her arrival in Delhi on January 15, 2014, and alleged that he had tried to "mislead" the investigation.
The police had further said that Narain remained silent on the "issue" on which Pushkar wanted to "expose" Tharoor in a press conference which was to be held on January 17, 2014.
It had also said the mobile phone recovered from Narain belonged to Tharoor who could not explain the reason why he was keeping it.
The police had mentioned similar reasons with regard to Bajrangi and said he was present in the hotel on January 16-17, 2014 and was acquainted with the facts of the case.
"He (Bajrangi) did not disclose about the injury marks present on the body of deceased Sunanda Puskhar. He also did not disclose about relation of Shashi Tharoor with Pakistan journalist Mehr Tarar which was an apple of discord between the couple," it had said.
Tharoor has been questioned thrice in this case so far. Pushkar was found dead in the hotel suite on January 17 last year, days after a public spat on Twitter where she accused her husband of having an affair with the Pakistani journalist.
In the first week of January this year, police claimed that Sunanda Pushkar (51) was poisoned, and registered a murder case against unknown persons.
A Special Investigation Team, formed to probe the case, is learnt to be looking into a possible link with the multi-million dollar Indian Premier League.