Early returns from the Wisconsin State Supreme Court race showed a dead heat Tuesday night in an election with significant implications for Gov. Scott Walker's law to curtail collective-bargaining rights of most public employees in the state.

The race, between conservative incumbent David Prosser and left-leaning assistant district attorney JoAnne Kloppenburg, is widely seen as a proxy war over Mr. Walker and the union law.

When the bill passed last month, tens of thousands of people demonstrated against it in the state capital.

Two hours after polls closed, Mr. Prosser was leading 51% to 49% with 61% of the votes counted, according to the Associated Press.

The stakes are high because the law is expected to end up before the state Supreme Court which has generally split 4 to 3 with a conservative voting block in the majority. The race is technically non-partisan, but Democrats have spent heavily in support of Ms. Kloppenburg in the hopes that she would tilt the court's balance and vote to strike down the law. Conservatives and business groups have supported Mr. Prosser.