Teachers at the New York French American Charter School in Harlem will be allowed to unionize, a state agency decided on Wednesday, overriding objections from the school’s administration.

The United Federation of Teachers had filed a petition with the state’s Public Employment Relations Board in December to represent teachers and other staff members at French American, a Harlem charter school with bilingual instruction that opened in 2010. But the school challenged the petition, arguing that three teachers had been coerced into joining the union.

On Wednesday, the Public Employment Relations Board ruled that French American had no evidence that any teachers had signed union cards against their will. Even if they had, a majority of teachers still favored unionization, wrote Monte Klein, a board official, in the decision.

The decision makes French American the 16th of the city’s 136 charter schools to join the city teachers' union.

Dick Riley, a spokesman for the U.F.T., said in an e-mail message that the union has faced opposition to unionizing teachers from a majority of those schools, and has had to ask the employment board to intercede. “Organizing continues at other schools,” he added.