A narrow majority of voting workers for a Ronkonkoma-based school bus company that transports 15,000 Long Island children each school day voted Saturday to reject a final contract offer and vowed to strike.

Union members haven't set a strike date, but are expected to have an emergency meeting Sunday to determine logistics and timing. Teamsters Local 1205 officials instructed workers to go to work Monday, but to be prepared in the event a union representative is waiting, ready to lead them in a picket line.

But officials for Baumann & Sons Buses Inc. questioned whether enough union voters turned out to approve the work stoppage.

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Local 1205 president Timothy Lynch said members approved the strike against Baumann and its affiliate, Acme Buses, 302-293 -- a nine-vote margin out of 595 cast. The vote was held at the IBEW Local 24 Union Hall in Hauppauge.

The Teamsters' constitution requires that at least half of eligible union workers participate for a strike vote to be legitimate, otherwise a two-thirds majority is necessary.

By that rule, if more than 1,190 eligible union members work for the company -- twice the number of votes cast Saturday -- the union would not have had enough votes for a simple majority approval of a strike. In that case, by default of the low turnout, Saturday's vote would have approved Baumann's three-year contract proposal.

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Glenn Smith, an attorney representing Baumann, said company officials believe they employ more than 1,200 union workers, and that the vote failed to approve a strike.

"Given the relatively low turnout of the vote . . . and the razor thin margin of the rejection, we would hope that there would be another vote called for immediately and that it would be held at each yard, when employees report to work or return from their routes, so that the entire workforce can truly decide what they want to do," he said in a statement. "We would do everything in our power to facilitate that on any day this week."

But union officials said fewer than 1,035 dues-paying members work for Baumann/Acme, meaning the narrow margin was enough to seal the strike.

"I am certain -- no doubt whatsoever -- that a majority of our Baumann/Acme members voted on the 'last, best and final offer' and a majority rejected it," Lynch said.

The outcome leaves many parents and officials at roughly 35 school districts in Nassau and Suffolk counties without the certainty the vote was expected to deliver.

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The effects of a strike would be felt unevenly across the Island, as some schools contract with the company for a few buses, while others -- such as the Commack school district -- rely on Baumann/Acme for all of its transportation needs.

A number of districts have taken steps to notify parents of a potential strike since the union sent them an Aug. 26 letter regarding a possible strike.

Some districts have found contingency plans to work around a work stoppage, but many have notified parents they will be responsible for their children's transportation in the event of a strike.

The company also drives for many of the BOCES centers, special education centers and private and parochial schools to which school districts by law must supply student transit.

Negotiations ended in early October, when the company announced it had made its best possible offer.

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"We've gotten the company to go much further toward justice than it wanted to, but there are a few central issues that need to be addressed," Lynch said in a statement.

Officials for Baumann said the final offer would have had the company spending 12 percent to 14 percent more on employee costs, including benefits and raises, starting in the final two years of a three-year contract for most workers.

The union had demanded higher pay, increased contributions for health and other benefits and better working conditions.