Saturday's snap vote, triggered after minority Liberal premier Jeremy Rockliff lost a no-confidence motion in early June, is the island's second in 16 months.
The 11-year Liberal government was plunged into minority in 2023 when two MPs quit the party and was returned in minority at the March 2024 poll.
Polling places opened at 8am (AEDT) but more than one-quarter of Tasmania's 412,000 registered voters had cast their ballot early.
Election-eve polling by YouGov has the Liberals (31 per cent) and Labor (30 per cent) neck-and-neck, with neither reaching the 18-seat mark required for majority.
It represents a dip in support for Labor from YouGov polling in early July.
Backing for independents (20 per cent) has risen while the Greens (16 per cent) have remained stable.
In a hung parliament, Labor leader Dean Winter was backed by 55 per cent of respondents over Mr Rockliff (45 per cent) as preferred premier.
Both leaders have ruled out doing a deal with the Greens to govern, but Mr Winter has kept the door ajar for an informal supply and confidence arrangement with the minor party.
Mr Rockliff and Mr Winter have said they were prepared to work with "sensible" independents.
There have been no big-spending promises in a campaign held under the shadow of ballooning budget debt, forecast to more than double to $13 billion in 2028.
Mr Rockliff's final pitch to voters on Friday was hinged on his party's experience and Tasmania's 3.8 per cent unemployment rate, the lowest in Australia.
"We were elected to do a job in March 2024 ... and we've got the leadership to get on with the job," he told reporters.
Mr Winter, whose party holds 10 seats compared to the Liberals' 14, said it was time for a fresh start.
He lashed Mr Rockliff's financial management and the botched delivery of two new Spirit of Tasmania ships, two of the reasons for the no-confidence motion.
"They've mismanaged major projects ... (and) our finances are the worst in the nation,' Mr Winter said.
Mr Rockliff's signature campaign pledge to create a state-owned insurer on Friday copped a scathing assessment from Treasury which said it lacked detail.
The Greens, who hold five seats, have vowed to "push hard" in opposition to a new $945 million stadium in Hobart that is supported by the Liberals and Labor.
The 2024 poll elected three independents. Kristie Johnston and Craig Garland, who are against the stadium and voted no-confidence against Mr Rockliff, are expected to return.
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