"Modi should come clean on the charges of snooping on a woman in Gujarat," the party Central Secretariat said in a statement here.
"Snooping is different from providing security", CPI further stated in reference to BJP's claims that the surveillance was being done to protect the woman.
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Demanding a thorough judicial inquiry into the "objectionable act", CPI said that, "the nation wants to know the truth behind snooping on a young woman upon the orders of the Chief Minister of the state.
"The role of Amit Shah, who is notoriously famous for his involvement in the fake encounter cases, also should be transparent in this case," CPI added.
The party also strongly condemned the reception given by BJP in Agra to two of its legislators who have been charge-sheeted in the Muzaffarnagar communal riots cases.
"BJP is directly insulting the memory of the innocents who were killed, injured... By honouring those (leaders). The real face of BJP is exposed with this shameful act of honouring the accused," it alleged in a statement.
It also asked Modi as to the reason for his silence on the government's decision to double gas prices, alleging that the move was "intended to help a particular corporate company".
"People are appalled to know that both BJP and Congress work in favour of corporate interests, allowing them to loot the nation at will," CPI said.