The 62-year-old had allegedly parked his car near a bus stand close to his house, sources said.
“He seems to have used his own licensed revolver. There was no suicide note found. A family problem appears to have pushed him. We are investigating,” a police officer said.
Investigators are planning to look into his call records for clues.
Mr Rajendran was nominated to the Rajya Sabha by the AIADMK in the year 1996. In 2000, he switched to the DMK which appointed him treasurer of the Tuticorin district unit around that time.
His family says he was involved in various businesses including hotel and transport.