The Haryana Police has booked all three, who are considered close aides of rape-convicted sect chief Gurmeet Ram Rahim Singh, on charges of sedition, inciting violence and criminal conspiracy.
The DGP said there was no pressure on the police and the investigation into the matter is being done independently.
"Private properties of Honeypreet, Pawan Insan and Aditya Insan would be attached," he said.
Mr Sandhu said that investigations into the August 25 violence that took place after the verdict of the CBI court on the Dera chief are heading in the right direction.
"Arrests are being made on the basis of evidence. As many as 1,100 persons have so far been arrested, including 44 from Sirsa, whose involvement was confirmed," the DGP told media in Sirsa town, 260 km from Chandigarh.
He said that the police have released a list of 43 persons who were involved in the violence that took place in Panchkula.
"Search operation is under way to nab three most wanted, including Honeypreet, Pawan Insan and Aditya Insan. International alert has been issued on them and teams are conducting raids to nab them," he said.
There were reports that Honeypreet could have escaped to Nepal and could try to flee to another country.
Aditya Insan, chief spokesman of the Dera and a close aide of the sect chief, has been absconding since August 25. On Ram Rahim Singh being quizzed by the police regarding Honeypreet, Sandhu did not give a direct reply.
"Police investigation is heading in the right direction, and whosoever required, would be interrogated," he pointed out.
Asked why Honeypreet was not arrested earlier as she had accompanied Ram Rahim to Panchkula and later to the Rohtak jail, the DGP said: "Until August 25, no case was registered against Honeypreet. But after the arrest of Surender Dhiman, Honeypreet was found to be accused of provoking violence. Therefore, a case was registered against her and search was on to nab her."
Mr Sandhu said the police had information that after the violence in Panchkula, Honeypreet came to the Dera headquarters in Sirsa. He said that as per the Punjab and Haryana High Court orders, a search operation was carried out in the Dera headquarters campus under supervision of the court commissioner who would submit his report to the court on September 27. One copy of the report would be given to the Haryana government.
"Further action will be taken according to the court orders," he added. Referring to the revelations of Honeypreet's ex-husband Vishwas Gupta on the relationship between the Dera chief and Honeypreet, the DGP said that Gupta had met the Panchkula Police Commissioner, but he had not given any complaint in writing. If any written complaint is received, police would include it in the investigations, the DGP said.
Convicted by the CBI court in Panchkula on two counts of rape of female disciples in 1999, Ram Rahim was sentenced to 20 years of rigorous imprisonment by the CBI court, and a fine of over Rs 30 lakh.
His conviction led to violence in Panchkula and Sirsa in Haryana, leaving 38 people dead and 264 injured. Isolated incidents of violence were also reported from Delhi and several other places in Punjab.