PM Modi's Bharatiya Janata Party (BJP) has fielded former policewoman Kiran Bedi as its pick for chief minister.

But polls suggest she is likely to lose to Arvind Kejriwal, an anti-corruption activist who heads his own party.

Mr Modi won convincingly in last summer's general election, and has ridden a wave of popularity ever since.

Over 13 million people are eligible to vote at over 12,000 polling centres in the state assembly elections.

Security is tight and more than 55,000 police and paramilitary have been deployed.

Official results for the 70-member state assembly are due on Tuesday.

At the scene: Sanjoy Majumder, BBC News, Delhi

A few months ago, everyone here expected Narendra Modi's BJP to easily win this poll, adding another feather in the cap of the formidable Indian prime minister following his massive win in last year's general elections.

But it has become a surprisingly tight contest after an energetic campaign by the Common Man (Aam Aadmi) Party led by its low-key leader, Arvind Kejriwal.

In particular, the party has appeal among working-class voters concerned about issues such as rising prices, jobs and corruption.

The BJP is banking on the prime minister's charisma and pledge of bringing in economic reforms and foreign investment.

In recent months, the BJP won a string of state assembly elections.

But correspondents say a tough fight awaits them in Delhi, where several surveys have put Mr Kejriwal's Aam Aadmi Party (AAP) ahead of the others.

The Congress party, which ran the Indian capital for 15 years until 2013, is predicted to come a distant third.

Delhi has been without a government since Mr Kejriwal, the former chief minister, resigned last February, angered that his anti-corruption bill was blocked.

Since then the state has been governed directly by the federal authorities.

Ms Bedi and Mr Kejriwal worked together during the anti-corruption campaign, led by social activist Anna Hazare, but the two have since developed an intense rivalry.

During weeks of hectic campaigning in Delhi, both candidates promised to bring in good governance, end corruption and make Delhi safe for women.

In the previous Delhi election held in December 2013, the BJP won the most seats but fell short of a majority, leaving the AAP - which came second - to form a coalition with the Congress party.

Mr Kejriwal resigned on 14 February after 49 days in office, however, after opposition politicians blocked a bill that would have created an independent body with the power to investigate politicians and civil servants suspected of corruption.