Mexico City ? The cloth patches in green, blue and white are everywhere, clamped tight over the mouth and nose of teachers, toddlers, policemen and drunks. Even the statue at the church of St. Jude, patron of lost causes, has been fitted with a light-blue surgical mask to ward off swine flu.

But do they work?

While Mexico has handed out millions of facial coverings, U.S. officials have held off, saying there is little evidence of their effectiveness. Some doctors warn they might even be harmful, causing people to take risks — like venturing into crowds or neglecting to wash hands — in the mistaken belief that the mask protects them.

The ubiquitous masks give an eerie, unsettling air to this overcrowded city, as if 20 million people have entered a scene from some kind of apocalyptic future.

They’re also a reminder of an equally frightening episode: Technicolor versions of those dotting scratchy black and white photographs from the 1918 Spanish Influenza epidemic, which claimed up to 50 million lives worldwide.

Soldiers hand them out at subway stations. Pharmacies and hardware stores can’t keep them in stock. Newspapers have begun running front page instructions on making do-it-yourself mouth coverings. President Felipe Calderon proudly boasted over the weekend that more than 6 million masks have been distributed.

“They must be worn when one is out in public or in a closed, crowded space,” Health Secretary Jose Angel Cordova insisted Monday, while acknowledging in the same breath that the government-distributed masks are too porous to eliminate all risk.

“They still offer enough protection as a public health measure,” he offered.

U.S. health officials give very different guidance. The Centers for Disease Control and Prevention said there is not a lot of evidence that masks do much good, and have pointedly not recommended their use by the general public. Swine flu is thought to be transmitted in much the same way as seasonal flu, by touching something with the virus and then passing it to the nose or mouth or through coughing or sneezing.

Experts say people who come in close contact with known swine flu patients should wear high filtration masks like those used by health professionals, which are more effective but also more expensive (about a dollar) and generally unavailable in Mexico City. But even these masks, which filter out fine particles carried in the air, must be used properly to give real protection.

“The evidence that masks work is relatively weak,” said Peter Sandman, a New Jersey-based consultant in crisis communication. Still, he was loath to criticize the Mexican government, because mask-wearing also can have psychological benefits.

“It’s not dumb to give people things to do, even if those things are only slightly effective, because it will make those who are anxious feel calmer, and those who are too nonchalant take the threat more seriously,” he said.