His remarks came while replying to Gandhi's "chowkidar chor hai" taunt apparently aimed at Prime Minister Narendra Modi, saying Rahul and the entire Gandhi family are "thieves".
Satti has been booked under Section 294 of the Indian Penal Code. The case pertains to obscene acts and songs.
The Congress on Tuesday held statewide protests over the "obscene slur".
Defending him, state BJP General Secretary Randhir Sharma said: "Satti's video, which was in circulation in the social media, was a doctored one and the Congress was trying to take electoral mileage out of it.
Himachal Pradesh will go to the polls on May 19.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)