Let’s say the 7-year-old daughter of illegal immigrants working in a big American city wakes up this morning with a high fever and a rash.

Is it in that city’s interest for the little girl to receive treatment at a local public clinic or hospital? Or is that community better off if the child’s parents try to treat her at home because they fear a doctor would ask about their immigration status – and report them to the federal government if they couldn’t prove they are here legally?

Before you answer, recall that in the 1982 Plyler vs. Doe decision, the Supreme Court ruled that children of illegal immigrants have a constitutional right to public education. That means whether that child is examined to determine if her illness is contagious, she soon will be back in a classroom of other 7-year-olds – many, in all likelihood, American citizens.

In most places, for most people, this would not be a hard call. Leaving aside any question of compassion toward the girl, the community’s public health is clearly served if she is treated before she infects anyone else.

Likewise, most people would agree that communities are safer if illegal immigrants who have been the victims of crime, or possess evidence that can help solve a crime, can talk to police officers without fear of being quizzed about their status.

These are the judgments that have prompted Los Angeles, New York and dozens of other major cities to adopt policies that in varying ways discourage municipal workers from assessing the immigration status of people using local services and sharing such information with federal immigration officials.

They also are the judgments that have provoked the sharpest clashes yet between the two leading GOP presidential contenders, former Massachusetts Gov. Mitt Romney and former New York City Mayor Rudolph W. Giuliani.

Romney charges that these city policies encourage illegal immigration by offering the undocumented “sanctuary.” He proposes to cut off federal funds for cities that adopt them and calls New York’s approach under Giuliani especially egregious. “New York City was the poster child for sanctuary cities,” Romney insists.

The disputed New York policy was adopted in 1989 by Mayor Ed Koch, a conservative Democrat, and later reaffirmed by Giuliani. The policy generally prohibited city workers from reporting information about immigrants’ legal status to federal officials. But it explicitly required police and other city workers to “cooperate with federal authorities” in investigating illegal immigrants suspected of a crime, including fraudulent attempts to obtain welfare benefits.

In 1996, the Republican Congress outlawed outright city bans on reporting immigration status to federal officials. Giuliani challenged the law in court and lost. Under Giuliani and his successor, Michael Bloomberg, New York then evolved toward a “don’t ask, don’t tell” policy, in which city officials no longer are forbidden from sharing information with Washington but are barred from inquiring about the immigration status of people using city services, except when it’s relevant to assess eligibility.

Giuliani defends his decisions but is so determined to appear tough on illegal immigration that his advisers, incredibly, won’t say whether he opposes Romney’s call to punish cities that do what Giuliani did as mayor. Giuliani should find some backbone because Romney’s idea would be counterproductive. His criticism draws on a legitimate concern: After 9/11, the nation has a greater incentive to identify everyone inside its borders, either legally or illegally. But turning city workers into immigration snoops won’t advance that goal.

If a mayor announces that he will check people’s papers at police stations, school admission offices and emergency rooms, illegal immigrants are unlikely to line up in those places to be discovered and deported. They are more likely to abandon those services – with dangerous consequences for all city residents.

Some cities, by condemning federal immigration raids, have carried the “don’t ask, don’t tell” impulse to excess. But Romney has overreached too with his threats against “sanctuary cities” such as New York. Romney’s aides won’t say what New York should have done differently in its policy toward illegal immigrants. Maybe that’s because the city, like many others, chose the most practical response available.