NEW DELHI — A handout for new teachers at this city’s exclusive American Embassy School, an academic oasis for children of American diplomats and other expatriates, offers some unusual guidance to female teachers whose husbands will also be teaching at the school.

“The female spouse should not state that she will be working,” the handout states, instructing spouses to list their occupation on visa applications as “housewife,” adding that “no sexism is intended on our part.”

That advice, which top Indian officials say is illegal, has ensnared the American school, a cherished institution among foreigners living here, in a growing diplomatic spat between India and the United States that began last month with the arrest in New York of Devyani Khobragade, an Indian consular official, on charges of visa fraud and making false statements in connection with her employment of a domestic worker.

The arrest and her resulting strip-search shocked the Indian diplomatic corps and generated about as much outraged commentary in the Indian news media as the beheading last year of an Indian soldier on a disputed border with Pakistan.