The special investigating team on Wednesday questioned three witnesses, including Srirangam-based woman Usha and a 'swamiji', in connection with the murder of Sankararaman, a Kanchi Mutt official.
Kanchi Shankaracharya Jayendra Saraswathi has been arrested in the murder case.
Usha had presented herself before the police on Tuesday.
She told newsmen after the questioning that she was asked the same questions that the police put to her a day before the SIT session. She said she had produced records in support of her illness and a copy of the passport application.
"I have now been cleared by the police", she claimed.
The police said she was very cooperative during the interrogation and said she would have to present herself as a witness during the trial.
Muralidhara swamiji, popularly known for his discourses on TV channels, was also summoned by the police for interrogation.
The police said the interrogation was only to know details of his connections with the Kanchi Mutt.
The third person to be summoned was Nalini, whose daughter Yuvashri, who was staying in the hostel run by the Kanchi Mutt, died in July under suspicious circumstances.
Sankararaman's letters, complaining about the mutt activities, details of which were recovered by police, had implied that the girl had died under suspicious circumstances. Nalini was questioned in this connection.
The police said Yuvashri's mother and uncle stated that the 11-year-old girl was a "weak and sickly child" and they suspected nothing mysterious about her death.
Police also affirmed that the mother and uncle had no complaints in this regard and the police were only going through the complaints arising from late Sankararaman's petitions as a matter of routine.
"No case has been made out," they said.
Meanwhile, in an intensified bid to conclude the investigations, the special investigation team personnel will visit Andhra Pradesh, Karnataka and Tirunelveli in Tamil nadu, according to sources.
The sources said 'Appu', the main accused in the Sankararaman murder case, would be arrested in a couple of days.
An inspector had been appointed to pursue the case of death under mysterious circumstances of two Kerala boys who were studying in the Mutt's Veda Pathasala two decades ago.