Special judge of a Protection of Children from Sexual Offences (POCSO) court Om Prakash Mishra granted bail to Prajapati, Vikas Verma and Amrendra Singh alias Mintu.
The court asked Prajapati to furnish two sureties of Rs 1 lakh each and a personal bond of the same amount.
An FIR was registered against Prajapati and six others on February 17 on a Supreme Court directive.
Prajapati was then a minister in the Akhilesh Yadav led Samajwadi Party government in Uttar Pradesh.
After being on the run for nearly a month, Prajapati (49) was arrested from the Aashiyana area here on March 15 and was sent to jail for allegedly raping a woman and attempting to rape her minor daughter in 2014.
The six others had been arrested earlier.
Prajapati had approached the Supreme Court to get a stay on his arrest. But the Apex court asked him to approach the court concerned.
The former minister had said that he was prepared for a Narco test to bring out the truth and also demanded a similar test on the minor victim.
The allegations against Prajapati were raked by the BJP during the state assembly elections to attack the then Akhilesh Yadav led government.
The Supreme Court order to file a police complaint against Prajapati had come just two days before the third phase of polling in the seven-phase state elections which saw Samajwadi Party winning only 47 of the 403 assembly seats while the BJP and its allies bagged 325 seats.
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