The 142-year-old cathedral here, which was vandalised allegedly by right-wing activists last week, has been targeted for the second time since 2008.
The parsonage in the Saint Peter and Paul Cathedral's premises was attacked on Friday night.
Parts of the Cathedral, situated in Cantonment area, were torched on September 12, 2008 but attackers remain unidentified till date. Sameer Kulkarni, the lone man tried for the arson, was later discharged by a court here.
Mumbai ATS, while quizzing Kulkarni, pointsman of Abhinav Bharat, a Hindutva outfit, for Madhya Pradesh learnt he was allegedly behind the arson.
Kulkarni, an accused in the Malegaon bombings, was later handed over to Madhya Pradesh Police and brought here to stand trial.
However, he was later discharged in the arson case, his lawyer Dipak Panjwani told PTI.
The entire altar of the Cathedral was burnt down. But even after nearly seven years, the guilty has not been punished, a Catholic priest said.
Police appear to have given up on the case in absence of credible leads and sought its closure.
"As we couldn't get leads even after toiling hard in the Church burning case, we have petitioned the competent court to close the case. We moved an application for closure some 6 months ago. Right now, I am not aware of the status of the case," said Cantonment Police Station In-charge Inspector Arvind Choubey.
