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.
All opinion polls point to neither the Liberals, who hold 14 seats, or Labor (10) boosting their support to reach the 18-seat mark for majority.
Election eve polling by YouGov has the Liberals (31 per cent) and Labor (30 per cent) neck-and-neck, with Labor dipping from a survey by the same company in early July.
Backing for independents (20 per cent) has risen while the Greens (16 per cent) have remained stable.
Mr Rockliff and Labor leader Dean Winter have ruled out doing a deal with the Greens to govern, but the latter has kept the door ajar for an informal supply and confidence arrangement with the minor party.
Mr Rockliff and Mr Winter have said they are prepared to work with "sensible" independents.
Speaking at a cafe in Hobart alongside Labor candidate John Kamara, Mr Winter said he was content with his campaign.
"Tasmanians have seen 11 years of chaos, dysfunction ... I think they're looking for change," he said.
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.
The no-confidence motion against Mr Rockliff, put forward by Labor and supported by the five-seat Greens and three crossbenchers, was critical of the budget and a bungled ferry delivery.
Another key issue has been plans for a $945 million Hobart stadium, which is backed by the Liberals and Labor but opposed by the Greens and several crossbenchers.
Mr Rockliff once declared he was prepared to be sent back to the family farm by voters in his pursuit of the stadium, which is a condition of Tasmania's licence for an AFL team.
"I'll have to learn how to grow spuds again if that's the case," he said on Saturday after voting in Sassafras in the northwest.
"The important thing is you stand up for what you believe in."
Incumbent Liberal MP and former senator Eric Abetz was served a democracy sausage by Labor candidate and union boss Jessica Munday south of Hobart.
"The parliament was seen as not working and unfortunately that was because of independents and the Greens," Mr Abetz said.
The 2024 poll elected three independents. Kristie Johnston and Craig Garland, who are against the stadium and voted no-confidence in Mr Rockliff, are expected to be returned.
It could be weeks for the final count to be completed, with the last postal votes not expected to arrive until the end of July.
More than one-quarter of Tasmania's 412,000 enrolled voters cast their ballot early.
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