The new online facility to issue birth and death certificates was launched in the Madurai Corporation earlier this month.
The computer generated certificates were "issued" by the Corporation Health Department officials through the online facility recently.
Following a complaint from Corporation officials, Commissioner of Police Sanjay Mathur directed the Cyber Crime Police to register cases under IPC and Information Technology Act, 2008.
According to the complainant, some unidentified persons had gained entry into the computer room in the Corporation office and issued the fake death certificates.
Meanwhile, Annadurai also gave a complaint to city Police Commissioner about the matter.
Madurai Corporation Mayor V V Rajan Chellappa, however, refused to comment on the matter.