The film, directed by Prakash Jha, also stars Arjun Rampal, Abhay Deol and Esha Gupta.
Patil told the Hindustan Times: "I had sent my pictures to the casting agent some six months before they called me. I auditioned along with many known faces, but still managed to get the part.
"I am a trained Kathak dancer, so following the steps wasn't hard. But the song was more about sensuality and expressing through the eyes. I was wary of my performance initially, but Ganesh Acharya [choreographer] sir told me it was perfect."
Chakravyuh centres on a police investigation into communist groups in rural India.
Rampal said this week that he wants the thriller to educate young Indian audiences about politics.
He also recently claimed that actresses in Bollywood have no reason to be "insecure".
Watch the trailer for Chakravyuh below: