India's ruling Bharatiya Janata Party (BJP) of PM Narendra Modi is expected to win the most seats in the southern Karnataka state, exit polls suggest.
But they say it will fall short of winning a majority in the 224-member assembly.
The opposition Congress party, which until Saturday's election controlled the state, is in second place.
The poll is significant for both of India's major parties ahead of general elections next year.
More than 49 million people were eligible to vote in Karnataka - the last major bastion of the Congress party.
Karnataka is the hub of India's information technology industry and has a population of 64 million.
The official results of the election will be announced on 15 May.
Why is the election important?
The polls in Karnataka are being treated as a bellwether ahead of scheduled national elections in 2019.
Both Mr Modi and Congress party leader Rahul Gandhi, travelled across the state, addressing huge rallies.
Analysts believe that a loss in this election would spell disaster for the Congress party, which rules only three other states apart from Karnataka.
The BJP and its allies are in power in 22 of India's 29 states.
However, this is also a crucial election for the BJP, which has won in Karnataka only once before. The party has a limited presence in the four other southern states, where it is unlikely to contest an election without a regional ally.
Who are the key players?
The Congress' candidate is Karnataka chief minister K Siddaramaiah, who is running for re-election. He led his party to a huge victory in 2013, winning 121.
"We are going to secure 120 plus seats (in the 224-member assembly)," Mr Siddaramaiah told BBC Hindi's Imran Qureshi before the poll. "I am 100% confident because I am the chief minister."
BS Yeddyurappa, the BJP's candidate, was equally confident of winning - "There is no doubt that I will be sworn in as chief minister on May 17," he told BBC Hindi.
He led the BJP to power the first time they won in Karnataka in 2008 and served as chief minister.
The Janata Dal (Secular), a key regional party that has given the state two chief ministers in the past, could emerge as an important player after the poll.
The party is led by HD Deve Gowda, who was the prime minister of India from 1994 to 1996.
What were the key poll issues?
The powerful Lingayat community, a Hindu sect that comprises 17% of the state's population, was expected to play a decisive role in the elections.
It has traditionally voted for the BJP but that might change this time. A section of the community has been demanding that the sect be identified as a separate religion, distinct from Hinduism.
Mr Siddaramaiah's administration has declared the community a separate religion and expects to split their vote as a result.
The chief minister has also taken controversial decisions such as proposing a flag for the state and emphasising the use of the local Kannada language.
Apart from the state's water crisis and lawlessness, corruption is also a key issue.
Mr Yeddyurappa himself resigned from his post as chief minister in 2012 amid allegations that he abused his power.
An anti-corruption report in 2011 had indicted him in a mining scandal that cost the exchequer more than $3bn (£2.2bn).