In her complaint, Menon said that she had tweeted to the Mumbai Police Commissioner about Bhattacharya's use of "obscene" language on social media towards a woman journalist.
However, the singer responded to her tweet with indecent language, Menon said.
A case has been registered under IPC section 500 (punishment for defamation) and 509 (word, gesture or act intended to insult the modesty of a woman) of IPC and section 67 of the Information Technology Act, police said.
The singer had recently sparked controversy by tweeting that the murder of an Infosys techie in Chennai was the result of "love jihad". However, when a Delhi-based journalist objected to his tweet, the singer had allegedly replied with abusive comments.