The case had been registered on a complaint from one Durgeswari lodged at the Ponmalai All Woman Police Station here, police said.
Meera, son of former Environment Minister Mariam Pichai, had on June 17 resigned from the post of deputy Mayor on the orders of the party high command.
The woman in her complaint alleged that Meera promised to marry her and made her pregnant.
She was having a girl baby through him. However, now he was threatening her using goondas.