The notice, served to Mani at his home at Kunjithanni near here, asked him to let the investigators know within a week whether he was willing to undergo the polygraph test, police said.
Police had registered a criminal case and started a fresh probe into the murder of an INTUC activist in Idukki district 30 years ago in the light of Mani's speech.
While addressing a public meeting at Manakkad near Thodupuzha in the district a few months ago, Mani said his party had in the 1980s drawn up a list of political rivals to be eliminated and executed that, which sparked a raging controversy within and outside the state.
With Mani's speech causing deep embarrassment to even the central leadership of the CPI(M), he was removed as the CPI-M Idukki district secretary and suspended from the state committee in July last.
Mani's speech dealt a severe blow to the party's image in the state as it came when the CPI(M) was under a cloud over the murder of rebel Marxist and Revolutionary Marxist Party leader T P Chandrasekharan and was locked in a fierce fight with the ruling Congress-led UDF in an assembly bypoll.
The party, however, consistently held that physical annihilation of foes has never been its policy.
