The hand written letter, though not legible, reportedly contained abusive language, naming caste and also threatened them of dire consequences, they said.
The letter was handed over to Kumaralingam police station.
The dalit youth Shankar and his wife Kausalya were attacked by a gang with sickles in full public view on March 13 in nearby Tirupur district, resulting in the former's death.
Police said investigation will begin after going through the letter.