Chief Judicial Magistrate Rajiv Kumar rejected the bail application of the officer saying that it was beyond his jurisdiction to hear the matter.
Joshi was arrested from his Vasant Vihar residence here last evening. Later, he was produced before the CJM court from where he was sent to 14-day judicial custody.
According to sources, Joshi was arrested after a probe team, headed by Additional Superintendent of Police Mamta Vohra, got some crucial evidence against the officer.
The 29-year-old woman from Dehradun had lodged FIR with Pandav Nagar Police station in Delhi accusing Joshi of raping her. The alleged rape took place in a room in police line officers' club at Nainital.
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Police recorded statement of the woman after she filed the complaint in Delhi on November 22.
She has alleged in the FIR that she was introduced to Joshi by Congress leader Ritu Kandiyal and Dehradun SP (Rural) Bhandari had mounted pressure on her not to go public over the matter.
However, soon after the victim lodged the FIR, Joshi refuted the allegations and lodged a complaint against three persons, including the victim, at the city's Vasant Vihar police station, accusing them of blackmailing him and issuing threats to defame him.