Members of the union that represents nearly 12,000 Santa Clara County workers have voted overwhelmingly to authorize a strike amid negotiations with county officials.

The leaders of Service Employees International Union local 521 have not yet called for a strike or set a date for one. But the vote, which was tallied Friday night, authorizes union leadership to call a strike, said Mullissa Willette, an employee in the county assessor’s office and first vice president of the local.

Willette said about half of the local’s members cast votes during the 16-day voting period, 97 percent of which were in favor of the strike.

The union represents employees throughout county government, including social workers and maintenance workers, among many others. It also includes clerical staff, janitors and certain other employees of O’Connor Hospital in San Jose and St. Louise Regional Hospital in Gilroy, which Santa Clara County acquired this spring.

Members have been working without a contract since their agreement expired June 16.

Negotiations over a new contract began in January, but Willette said each side remains far apart in their proposals for employee pay, benefits and working conditions.

“We really are trying to resolve this — a strike is the last thing we want to do,” Willette said. “The county has the opportunity to avoid a strike right now, and we hope they do so.”

County negotiators are proposing a contract that would raise all members’ pay by 12.5 percent in total over five years, with additional pay increases for certain classifications of employees. Willette declined to detail the union’s counter-offer.

The union also filed a complaint last month with California’s Public Employment Relations Board alleging unfair labor practices, saying the county has failed to address staffing issues at the intake center for children under temporary custody, creating safety issues for workers and the children.

County Executive Jeff Smith said the union’s contract proposal was “not even close to something the county can afford,” and said negotiations will continue.

“We hope there is not a strike, we are meeting in good faith at the bargaining table, and I am very confident that eventually we will end up with a good contract,” Smith said.