Metropolitan Magistrate Purshotam Pathak reserved his order after hearing the brief submissions made by the counsel for complainant Vibhor Anand, a law student.
Anand had moved the court seeking directions to the Delhi Police to file an FIR against Kejriwal for making derogatory remarks against MPs in his speech in an election campaign rally in Ghaziabad in February.
Kejriwal had in his speech allegedly called MPs "rapists, murderers and looters", evoking sharp reaction from politicians.
In its Action Taken Report filed in April, the police had told the court it has forwarded the complaint against Kejriwal to Ghaziabad Police for necessary action since the incident took place in their jurisdiction.
It had said that the complainant be directed to approach Ghaziabad police for the action taken report on his complaint.
Anand had also told the court that he was receiving threats to withdraw his complaint against Kejriwal.