Chief Metropolitan Magistrate Ashish Aggarwal dismissed the politician's application and said sufficiency of material cannot be examined at this stage.
"I have heard the arguments. Investigation is at a nascent stage...In light of the fact that investigation is only at the initial stage, I do not deem it fit to grant bail to the accused person. The bail application is rejected," the magistrate said.
It also remanded Ramesh Bhardwaj, who was arrested earlier, in judicial custody till August 15.
"The accused persons have admittedly been subjected to lengthy and repeated interrogation... Police custody is not expedient and, therefore the said application is rejected," it said.
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During the hearing, Delhi Police opposed the bail plea of Chauhan, saying that the probe was at an initial stage and there was a possibility of the accused person influencing and threatening the witnesses.
Advocate Pradeep Rana, appearing for Chauhan, sought bail claiming that the MLA and others were falsely impilicated in the case on account of political rivalry.
He argued that there was nothing to suggest the involvement of the accused in abetting the woman's suicide.
"At the most, it can be alleged that Chauhan neglected in providing redressal to the deceased but that would not tantamount to abetment of suicide," Rana said.
Chauhan, along with others, was arrested on July 30 and he is the 12th AAP MLA who was arrested.