Fr Therakam, the former child welfare committee chairman, and the two nuns arrived before the Peravoor circle inspector with their lawyer and turned themselves in.
Sister Betty is one of the child welfare committee members, while Sister Ophelia is the superintendent of an orphanage in Wayanad.
Fr Therakam and the nuns are the co-accused in a case, where a minor girl was raped and impregnated by Fr Robin Vadakkumcherry, a vicar, in Kottiyoor.
The police had arrested Father Vadakkumcherry, the prime accused, last month.
The co-accused, who were on the run, have been booked for hiding knowledge of the rape and aiding the delivery of the baby in February.
The victim gave birth to a boy at a private hospital in Kuthuparamba, and the child was taken to an orphanage at Vythiri in Wayanad.
Fr Therakam is also accused of trying to help Fr Vadakkumcherry to flee the country.
The Kerala High Court had ordered the priest and the nuns, who were absconding since Vadakkumcherry's arrest, to surrender before the police.