WARSAW (Reuters) -- Poland holds local elections on Sunday which provide the ruling conservatives with their first major test at the polls since they won power a year ago.

Opinion polls suggest Prime Minister Jaroslaw Kaczynski's Law and Justice party and its allies in the coalition government will do well in voting for local councils and regional assemblies, especially in the countryside.

But the main opposition Civic Platform is expected to perform better in the major cities, which have been engines of Poland's fast economic growth.

The vote takes on an extra significance two years after Poland joined the European Union because the winners will have a decisive say on how billions of euros in EU funds are spent on infrastructure projects over the next four years. "We have to remember that it is the local governments which will be in charge of EU funds," Kaczynski told party faithful last weekend. "This time the ballot has more weight than (the last two times they were held) four or eight years ago."

The campaign has been dominated by how best to spend EU money and a range of local issues, although in the big cities party loyalties appear to be the major factor.

Some analysts say a good result for Law and Justice could encourage it to abandon its uneasy coalition with leftist and rightist fringe parties and call an early general election.

"If they do well, they may be tempted to dissolve parliament and call early elections next year," said Pawel Swieboda, director of demosEUROPA think-tank.

But victory for Civic Platform would be a humiliating blow that could undermine Law and Justice's efforts to consolidate power, less than a month after reaching a deal with its allies that narrowly prevented the coalition falling apart.

Just over 30 million people are eligible to vote to fill mayoral posts in the cities and 46,790 councilors' posts in counties, towns and cities and on regional councils. Second round run-offs will be needed in some districts on Nov. 26.

A survey by PGB polling group showed the ruling coalition has 40 percent support, ahead of the Civic Platform and their Peasant Party partners with 33 percent. The centre left, which joined forces after a disastrous result in the 2005 general election, can count on 15 percent of votes.

Opinion polls show Law and Justice candidates ahead in two of the mayoral races in the 18 biggest cities and Civic Platform leading in three. Most mayoral contests are dominated by incumbents with no clear political affiliation.

A run-off ballot will be held on Nov. 26 in mayoral races where no candidate wins more than 50 percent of votes.

A decisive battle will be fought in the capital, Warsaw, where the mayoral race is close. Surveys show Kazimierz Marcinkiewicz, Law and Justice's popular former prime minister and acting Warsaw mayor, is running neck-and-neck with Hanna Gronkiewicz-Waltz, a former central bank chief.

Previous mayor Lech Kaczynski, the prime minister's twin brother, owed his victory in last year's presidential election largely to his time at Warsaw city hall.