The woman handed over a letter to the Investigation Officer of CID, seeking a CBI probe into her allegations, a police spokesman said.
At present, the CID - Crime Branch of the state police is probing the matter.
More From This Section
Anjana, MLA from Nimbahera in Chittorgarh district, was booked for allegedly sexually exploiting a nearly 50-year-old woman since 1984 on the pretext of marriage and forcing her to undergo abortion, charges which he denied.
The case was registered against Anjana in Mundwa following an order by a local court in Nagaur district.
Following the court's direction, Anjana was booked under section 376 (rape), 313 (to force abortion against the will of woman), 370 (illegal confinement), 384 (threatening life) and 420 (cheating) of the Indian Penal Code.
The case has been transferred to the CID crime branch as it was related to a MLA of the state, a police official said.
Anjana has denied the allegations and claimed that the charges were baseless and were part of a political conspiracy.
He claimed that the woman had made similar accusations in 2000 and said they had been proven wrong by various agencies.