“I speak little English,” she said in a hesitant and heavily accented interview in her lawyer’s office. “But my English is fine for San Luis.”

Mrs. Cabrera may be able to get her point across in English, but whether she is proficient enough in the language to serve on the governing board of this bilingual border city has deeply divided the 25,000 residents.

What began as an effort by political opponents to block Mrs. Cabrera from the ballot for a seat on the City Council has mushroomed into an uncomfortable discussion of just how fluent Arizona officeholders need to be. Like many other states, Arizona has long required politicians at all levels to speak, read and write English, but the law fails to spell out just what that means. Is grade-school knowledge enough? Must one speak flawlessly? Who is to decide?