By John Rondy

MILWAUKEE (Reuters) - Wisconsin voters went to the polls on Tuesday for the first of a series of special elections prompted by the bitter partisan battle earlier this year over the collective bargaining rights of government workers.

But turnout, which was expected to be low, was off to a slow start in Shorewood, a suburb of Milwaukee and home to the Democratic Primary for the 8th Senate District.

"I don't know if it will pick up this afternoon or not," said Sherry Grant, Shorewood's Village Clerk. "We are looking at using less poll workers for the afternoon unless it picks up."

Tuesday's elections are Democratic primaries in six Republican-held state Senate districts. They are the first step in efforts to recall lawmakers on both sides of the union issue.

But the votes have a strange twist. The Democrats running in the primary are opposed by six Republicans who are running as Democrats. And while confusing, under Wisconsin law it is legal. Republicans are posing as Democrats to force the Democrats to hold primary elections and give the incumbents Republicans more time to campaign and raise money. The final recall elections will be in August.

Unlike many other U.S. states, Wisconsin has open primaries and no official party registration. So Republicans can run as Democrats and vote in Democratic primaries and vice versa for Democrats.

Normally, there's little reason to cross party lines, but the tactic could prove decisive in the state where the new law curbing the power of public sector unions catapulted Wisconsin to forefront of the national political stage.

The law, which was passed by the Republican-controlled legislature and signed by Governor Scott Walker in March, eliminated most collective bargaining rights for public workers in the state and required them to pay more for pensions and health coverage. It triggered the biggest opposition demonstrations in the state since the Vietnam War.

Walker said the compensation and bargaining rights were unaffordable in an era of soaring state budgets and defended the measure as necessary to help fix state finances.

Democrats said the measure was a blatant effort to weaken public unions -- one of the Democratic Party's biggest financial supporters.

If Democrats gain just three of the seats at stake once the final votes are cast, they will take control of the upper house and have a better chance to thwart Walker's far-reaching legislative agenda. Republicans will continue to have a majority in the lower house, or Assembly.

In total, six Republican senators who supported the anti-union measure, and three Democrats who opposed it, will be defending their seats this summer as a result of recall efforts.

(Writing by Karin Matz and James B. Kelleher; Additional reporting by David Bailey in Minneapolis, Jeff Mayers in Madison; Editing by Greg McCune)