More than 20 million are eligible to vote, with some 1,800 candidates contesting 187 assembly seats.
Five states are holding local elections over the next month – a major test for India’s governing Congress party.
The first round of polls, in Manipur over the weekend, was marred by violence when suspected rebels attacked a polling station, killing four people.
Among the dead in the north-eastern state were polling officials, reports say.
Tight security
As well as elections in Manipur, Punjab and Uttarakhand, voters in Uttar Pradesh and Goa will also vote in the next few weeks, with results due on 6 March.
Monday’s polls in the politically crucial northern state of Punjab are expected to see a keen contest between its ruling coalition – led by the regional Shiromani Akali Dal party – and Congress, which is the main opposition in the state. There are 117 seats in the state assembly.
Hundreds of policemen and paramilitary soldiers have been deployed in Punjab to ensure peaceful polling.
In mountainous Uttarakhand, the Hindu nationalist Bharatiya Janata Party (BJP) is fighting to gain a second term in power in face of opposition from Congress. The state has 70 assembly seats.
Prime Minister Manmohan Singh and his government have been on the defensive in recent months, as Congress struggles to get its anti-corruption bill through parliament