Police said DMK Councillor Anbumuthu had alleged illicit relationship with Deepa Mayilsamy, an AIADMK councillor.
Deepa was living separately as her husband severely warned her against the affair.
Anbumuthu found hacked to death in Deepa's house today while the woman hanging in another room which was locked from inside, police said.
Superintendent of Police Sonal Chandra and DSP Suriliyandi visited the spot. Further investigation was on, police added.