COLUMBUS, Ohio — A year after Republicans swept legislatures across the country, voters in Ohio delivered their verdict Tuesday on a centerpiece of the conservative legislative agenda, striking down a law that restricted public workers’ rights to bargain collectively.

The landslide vote to repeal the bill — 62 percent to 38 percent, according to preliminary results from Ohio’s secretary of state — was a slap to Gov. John R. Kasich, a Republican who had championed the law as a tool for cities to cut costs. The bill passed in March on a wave of enthusiasm among Republicans fresh from victories. A similar bill also passed in Wisconsin.

Across the country, several other Republican-backed measures were also dealt setbacks, including a crackdown on voting rights in Maine.

In Mississippi, voters rejected an amendment to the State Constitution that would have banned virtually all abortions and some forms of birth control by declaring a fertilized human egg to be a legal person.