The woman, whose husband was working abroad, had developed an illicit relationship with a milk vendor, her neighbour, they said.
As relatives condemned the illicit relationship, the couple left the house a few days ago.
Meanwhile, her husband lodged a complaint with police.
Even as the police were searching for the couple, the woman called the police and informed them that she was in love with the vendor and that they had decided to commit suicide.
Though police stepped up efforts to trace them, they received information early this morning that two bodies were found along the railway track near Kadayanallur in this district.