It also charged the Mamata Banerjee government with transferring police officials -- some considered close to Trinamool and others considered honest -- ahead of Assembly polls due in April-May to suit its requirements.
Party leaders Sitaram Yechury and Nilotpal Basu met Chief Election Commissioner Nasim Zaidi and handed over a memorandum.
In the memorandum, CPI-M said it has apprehensions that "huge sums of ill-gotten funds" from the ponzy scam could be used to influence voters.
Questioning the "partisan role" of police, the party also pressed for "measures to rectify this situation which puts the opposition in a largely handicapped situation."
They said certain areas such as the tri-junction of Birbhum, Bardhaman and Murshidabad districts are sensitive in nature and constitute a hub of "widespread violence."
"Special measures need to be initiated to neutralise such acts of frequent violence in this region," the memorandum said.