Franco Mulakkal, 54, was formally detained on Friday after police questioned him for three days in the southern city of Kochi.
The protesters held a torchlight protest against the police delay in arresting the bishop even after two days of interrogation.
He wrote the letter after Kerala police summoned him to appear before it for questioning in the case.
Earlier this month, she alleged that the bishop was using "political and money power" to "bury" the case and was seeking his removal in a fourth letter to the Vatican's representative in New Delhi.
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When asked whether Mulakkal can be arrested before September 25, the day his anticipatory bail plea will come up for hearing in the high court, the top police officer said, "I think, legally there is no problem". Franco Mulakkal had last week handed over administrative responsibility of the Jalandhar diocese to a junior priest in his absence ahead of his Kerala visit.
Mulakkal, who is the bishop of the northern Indian city of Jalandhar, has denied the accusations. The nun had claimed that most of the times it was unnatural sex. One of the nuns, while slamming the police's inaction in nabbing the accused said, "The police have repeatedly taken the statement of the victim nun, but they have taken Franco Mulakkal's statement only once". She said she had to approach police because church authorities did not act on her complaints.
The Catholic Bishops' Conference of India (CBCI) had said on Thursday that Pope Francis had temporarily relieved Mulakkal of his pastoral responsibilities, a decision welcomed by the protesting nuns who termed the development as the "first victory" in their fight against the former bishop.
The case comes at a time when the Christian community, which accounts for 19 percent of the state's population, is reeling under an erosion of trust as sexual abuse cases involving the clergy pile up.