"The security of the victim's family is continuously being monitored...Five policemen have been deployed at the house and a strict vigil is being maintained on all the visitors," SP (City) Dinesh Tripathi told PTI today.
"I am personally reviewing the security as the court judgement likely to come soon and officials are in touch with the family," the Superintendent of Police (SP) said.
The father of the victim said that he had complete faith in the judiciary and was confident that justice would be done.
Earlier this month, Judge Madhu Sudan Sharma of the Jodhpur court heard the final arguments from the prosecution and defence counsels for five months and reserved the order for April 25.
The teenaged girl had accused Asaram of sexual assault at his ashram in Manai village near Jodhpur.
The girl, who belonged to Shahjahanpur in Uttar Pradesh, was a student living in the ashram.
If convicted, Asaram faces a maximum sentence of 10 years.
He is also facing a rape case in Gujarat.
Earlier, the top court had refused to grant bail to Asaram on various grounds in the two sexual assault cases lodged in Rajasthan and Gujarat.
Two Surat-based sisters had lodged separate complaints against Asaram and his son Narayan Sai, accusing them of rape and illegal confinement, among other charges.