As state and local governments push to get employees to pick up more health care costs, some employees are pushing back.

On Thursday, a Michigan judge heard arguments in two of three lawsuits filed by public-school unions and retirees who opposed a new law that for the first time required them to contribute toward their health-care benefits.

Michigan is among several states struggling with record budget deficits that want employees to take on a greater share of the burden of ballooning health-benefits costs.

The states’ search for financial options come amid a growing awareness of the gap in benefit contributions between public and private employees. A handful of states have made changes this year, including Kentucky, Connecticut and Texas, and they join a growing number of governments that have cut health benefits in recent years without major challenges.

But in Michigan, the trend has met firm resistance. At issue is whether state workers will now pay 3% of their monthly salary toward a trust that would fund retiree health-care benefits. Previously, they had paid nothing. The change will mean that the workers pay $300 million of the more than $920 million in health-care costs projected for the next fiscal year…

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