Police spokesperson, DCP Pranaya Ashok told that the action has been initiated by Azad Maidan Police Station.
The 51 were among hundreds who took party in a rally, the Queer Azadi Mumbai (QAM), organised by various LGBTQIA groups led by Humsafar Trust on Saturday at Azad Maidan.
QAM spokesperson Harish Iyer told that the persons questioned and booked by the police were unauthorised people who had entered the venue and maintained that the QAM had nothing to do with them.
Earlier on Monday, as some videos of the group raising slogans in support of Sharjeel Imam in the rally went viral, opposition Bharatiya Janata Party (BJP) attacked the Maha Vikas Aghadi govt while one senior leader lodged a complaint with the police demanding action against those who had supported Imam.
Leader of Opposition Devendra Fadnavis demanded to what "what was going on and why the Maharashtra govt was keeping silent in the matter".
BJP'S state Vice President Kirit Somaiya threatened to stage a dharna outside the Azad Maidan Police Station if the police failed to book such persons within 72 hours.
Among those booked are reported to be several girls who took part in the QAM rally, but the QAM has dissociated itself from their actions.
Police have slapped charges under Section 124-A (sedition) of the Indian Penal Code, and other sections, against the group, including activist Urvashi Chudawala.
The group was seen carrying posters with Imam's picture and raising slogans promising to complete his unfulfilled task.
Earlier on Monday, following the uproar, Home Minister Anil Deshmukh had said that the police were examining the issue before initiating suitable action in the matter.
( With inputs from IANS )