The video, shot on the Lakshman Jhula bridge, was posted on the social media.
Police arrested the French woman on Thursday and later released her on bail.
Her mobile phone was seized as part of the investigation, reports NDTV.
She apologised Sunday but denied being completely naked saying that she carried out the stunt to bring attention to sexual harassment.
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Police said Saturday that the 27-year-old – identified as Marie-Helene – faced charges under the internet laws after posting footage of herself on the Lakshman Jhula, made famous by the Beatles in the 1960s and which remains a draw for backpackers and yoga practitioners.
"She told us she sells bead necklaces online and the shoot was aimed at promoting her business," said RK Saklani, the local police station chief.
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