By Amy Sawitta Lefevre

BANGKOK (Reuters) - Most Thais are undecided about how they will vote next month in a referendum on a new constitution that the military government says will promote stability but which critics say will entrench military influence, a pollster said on Tuesday.

The Aug. 7 referendum is an important step for the government that took power after a 2014 coup as it tries to shape a political system after a decade of turmoil in Southeast Asia's second-biggest economy.

The government has stifled dissent and is particularly sensitive about criticism of the draft charter, curbing debate ahead of a vote that will be the first big test of its popularity.

But a one-sided information campaign has left many people dithering about how to vote and liable to make impulsive decisions, said Suwicha Pao-aree, head of polling at the National Institute of Development Administration university.

"Anything could happen," Suwicha told Reuters.

Suwicha said preparation for Thailand's referendum was very different to the campaign in Britain for a vote last month on whether to stay in the European Union or not.

"There has only been information from one side whereas in Britain both sides were allowed to take to the boxing ring and fight. The result is an undecided chunk of the population."

NIDA released a survey this week showing nearly 60 percent of 1,500 people polled around Thailand were undecided, 32 percent would vote in favor of the draft constitution and about 6 percent planned to vote against it.

The military government, which has promised an election next year, says the proposed constitution will heal divisions after years of rivalry between election-winning populist political forces and a military-dominated establishment wary of challenges.

Critics of the charter, including some major political parties and activist groups, say it would empower pro-establishment institutions at the expense of political parties.

Public opinion in the run-up to the referendum has been difficult to gauge because of a ban on campaigning, including a law stipulating 10 years in prison for criticizing the draft's content or disrupting the vote.

While activists say the charter would not heal underlying rivalries, some analysts say a vote in favor of it would be most beneficial for stability in the short term.

"This would be the least bad outcome from a short-term perspective as at least a roadmap to nominal democracy would be in sight," BMI Research said in a note on Tuesday.

Prime Minister Prayuth Chan-ocha has said an election will be held in 2017 regardless of the referendum outcome.

(Editing by Robert Birsel)