The incident occurred yesterday when the District Magistrate was not in his office, they said, adding that the trio have been admitted to hospital with minor burns.
The three youths, identified as Sunil, Anil and Raj Kumar are employed with a private agency where they are tasked with replenishing cash in bank ATMs, police said.
The trio told police that they had given Rs 74 lakh from the ATM cash to a youth who, however, later refused to return the same.
However, instead of reporting to police, the three youths went to the Collectorate and attempted self-immolation, officials said.
Police personnel and some people present at the scene foiled their bid, they said, adding an inquiry is on into the matter.