FRANKFORT — Health care workers in state hospitals voted Monday to join an alliance that includes the nation's largest public employee union.

        It was the first of at least four elections in which state employees in various categories can decide whether to be represented by a union on an advisory council to Gov. Paul Patton.

        The election had yet to be certified by the Labor Cabinet. But the winner appeared to be Health Care Workers United, an alliance of two unions — the American Federation of State, County and Municipal Employees, and the Service Employees International Union.

        The alliance got 594 of 785 ballots that were counted by La bor Cabinet officials Monday. About 1,700 health care workers were eligible to vote. Gary Moberly, the cabinet's election director, said 47 more ballots were not counted because the eligibility of senders could not be verified.

        Workers who wanted no union cast 117 ballots for “no representation.” A distant third, with 74 votes, was an alliance of the Steelworkers and Aerospace Workers unions and the Kentucky Association of State Employees, which already is affiliated with the American Federation of Teachers.

        AFSCME organizer Carolyn Klinglesmith said she expected the lopsided margin for her union's alliance. “We're the experienced union representing health care workers in this country,” she said.

        Mr. Patton in May signed an order creating his State Employee Advisory Council and authorizing nonsupervisory state employees to choose labor unions to represent them on it. The order, which could be undone by the General Assembly, does not allow collective bargaining, though Mr. Patton favors it. Nor does it allow state employees to strike, since that is forbidden under state law.

        Unions, or any other potential organizer, could bring about an election and be placed on the ballot by gathering signatures from 30 percent of eligible workers in a category.

        There are nine categories, one of which — corrections, parole and law-enforcement officers other than Kentucky State Police — is now balloting. Ms. Klinglesmith said AFSCME is unopposed in that election, which ends Nov. 6.

        AFSCME, with 1.3 million members, is aligned with the Teamsters and Auto Workers unions in efforts to organize other state-employee groups. Those with elections already scheduled are “labor and trades,” scheduled Nov. 13, and “employment and social services,” scheduled Dec. 18.

        For the first election, Ms. Klinglesmith said her union had organizing committees in all state hospitals, with especially strong efforts at Western State Hospital in Hopkinsville and at Oakwood, the state's largest and most troubled mental institution, in Somerset.

        In the last year, three former Oakwood employees have been indicted on charges of beating patients. Ms. Klinglesmith and John Thacker, a Service Employees International Union organizer, said their unions have been following the Oakwood cases closely.

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