The police vehicle carrying the bishop, who was sent to two-day police custody Saturday by a magistrate court in Pala, reached the St Francis Mission Home at 10.20 am and left the place after completing the procedure at 11.10 am.
In its remand report submitted in the court, police had said the nun was subjected to rape and unnatural sex by the accused at the guest house of St Francis Mission Home 13 times between 2014 and 2016.
The victim and her fellow nuns staying in the home were not present there when Mulakkal was brought.
Official sources said police planned to move an application in the court, seeking permission to subject the bishop to a lie detector as he was still reluctant to make the confessional statement.
The Kerala High Court Saturday had rejected the bail plea of the bishop and sent him to two-day police custody.
His lawyers had moved the application seeking relief, submitting that the clergyman was arrested after a three-day long interrogation by the probe team.
Opposing the plea, police had said his three-day custody was required to conduct his potency test and to recover the laptop, mobile phone and the dress used by the accused.
They said his body fluid and DNA samples were required to be collected as part of the probe.
Recording the submissions, the magistrate granted two-day custody of the bishop to police till 2.30 pm on Monday.
The Roman Catholic Bishop, who was arrested Friday night, was later taken to the Government Medical College Hospital, Kottayam, Saturday to perform these tests.
After completing the procedure at Kuravilangadu convent Sunday, Mulakkal was taken to the Police Club in the town.
He will be produced in the magistrate court in Pala at 2.30 pm on Monday.
In her complaint to the Kottayam police in June, the nun had alleged that Bishop Mulakkal raped her at a guest house in Kuravilangad in May 2014 and later sexually exploited her on several occasions.
The nun had said she had to approach the police as church authorities did not act on her repeated complaints against the clergyman.
However, the bishop has denied the charges.