In her tweets and during debates, Kishwar had alleged the senior bureaucrat was harassing the woman due to which her father asked for police protection. The suit filed last week has sought initiation of criminal proceedings against Kishwar.
Sharma has alleged Kishwar dragged his name in the scandal and tried to tarnish his image through comments on microblogging site Twitter and also TV channels.
The court is to decide if the matter falls under its authority. Additional Chief Judicial Magistrate H G Pandya heard arguments by Sharma's counsel regarding the jurisdiction of the matter and reserved its order for December 13.
Sharma has alleged Kishwar had made derogatory comments against him on her twitter account and during debates on news channels on the issue of alleged surveillance of a woman architect on orders of the then Minister of State for Home Amit Shah, a key aide of Gujarat Chief Minister Narendra Modi.
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Two investigative news portals, Cobrapost.Com and Gulail.Com have claimed, on the basis of taped conversation, that Shah had ordered the illegal surveillance at the behest of one "Saheb" in 2009.
Gujarat government has appointed a two-member commission to inquire into the scandal.