Prime minister Narendra Modi and his top ministers have campaigned hard to bring their Bharatiya Janata Party (BJP) to power in the big eastern state for the first time. They are facing a tough challenge from the Trinamool party, a regional group.
Elections in the state, also known as Bengal, are typically marred by deadly fights between party workers. Authorities have deployed nearly 80,000 additional central security forces to keep the peace during this year's voting, an eight-phase process that began on 27 March and ends on 29 April.
Previous rounds have been largely peaceful.
The BJP controls a dozen of India's 28 states, with alliance partners in several others. But it has never won power in Bengal, whose 90 million people make it the fourth most populous state. Wins in states dictate the position of a party in the upper house of parliament.