While Sarkar has been the chief minister of the state since 1998, his party the CPI-M has been in power in Tripura since 1993.
The CPI (M) and the country's ruling Bharatiya Janata Party (BJP) are pitted against each other in a direct fight.
The BJP's offensive in Tripura was led by Prime Minister Narendra Modi, who addressed four rallies in the Left-ruled state in the north-east.
Voting for the 59 out of 60 seats will be held at 3,214 polling stations.
While CPI-M claims to return to power, BJP President Amit Shah has asserted that the next Tripura government will be formed by the saffron party only.
Around 11% votes had been cast by 9am on Sunday, two hours after polling opened in Tripura, where the Communist Party of India (Marxist)-led Left Front faces a challenge from the BJP in its quest for a sixth successive term.
Results will be out on March 3.
The CPM has fielded 57 candidates, while the other Left Front constituents, the RSP, Forward Bloc and CPI are contesting in one seat each.
The Congress went it all alone in Tripura this time and contested from 59 seats. The Congress has fielded candidates in 56 seats.
An impressive 89.8% of the over 25.73 lakh electors came out to vote in Sunday's Tripura assembly elections, the Election Commission said on Monday.
However, the BJP has been criticised by the Left for tying up with the IPFT that wants a separate state of Tipraland to be carved out of Tripura for tribal-dominated areas, despite BJP saying that it is against the bifurcation of the state.
Meanwhile, the Election Commission has appointed a Special Observer while the authorities have sealed the worldwide and inter-state borders with Tripura.
While 300 companies of central armed forces were deployed, besides the state police, the BSF kept heightened vigil along the 856-km-long India-Bangladesh border in Tripura.
The first round lasted through Monday bringing more than 0.14 inches of ice, according to the National Weather Service. Strong to Severe Thunderstorms: Isolated storms may produce up to 1 inch hail and wind gusts up to 60 miles per hour .
It's been given a 15 certification by the BBFC due to its "very strong language, strong violence and sex references". Acclaimed actor Woody Harrelson takes on the role of the town's revered chief of police, William Willoughby.
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