BERKELEY, Calif. >> Leave it to Berkeley: This city, which has led the nation in passing all manner of laws favored by the left, has done it again. This time, the city passed a measure — not actually backed by science — requiring cellphone stores to warn customers that the products could be hazardous to their health, presumably by emitting dangerous levels of cancer-causing radiation.

Under the so-called Right to Know ordinance, passed unanimously in May by the Berkeley City Council, retailers are supposed to notify customers, starting in August, that “you may exceed the federal guidelines for exposure” to radio frequency radiation by carrying a cellphone in a pants or shirt pocket, or tucked into a bra. The potential risk, the warning continues, “is greater for children.”

Even supporters of the ordinance acknowledge that there is no definitive, scientific link between cellphones and cancer, although they argue that it may take years for cancers to develop. The American Cancer Society says that cases of people developing cancer after carrying cellphones may be coincidental or anecdotal. But some supporters are undeterred, noting that there are similar warnings in the fine print of cellphone manuals, and that the Berkeley warning is carefully written to reflect that language, albeit with additional cautionary words.

“We want to raise awareness,” said Ellie Marks, the founder of the California Brain Tumor Association. Marks does not live in Berkeley but brought her case here because, she said, “Berkeley has a reputation for taking progressive action.”

She said she is convinced that her husband, Alan, a real estate agent, contracted brain cancer at age 56 from often having a cellphone pressed to his ear.

Not surprisingly, the cellphone industry is not allowing such insinuations to go unchallenged. A few weeks after the law passed, CTIA-The Wireless Association, a trade group, filed a First Amendment lawsuit against Berkeley, charging that retailers cannot be forced to say something that is “false.” A hearing is set for Aug. 6 in federal court in San Francisco, and the ordinance will not go into effect until the matter is settled.

Theodore B. Olson, a lawyer with the firm of Gibson, Dunn & Crutcher who was solicitor general under President George W. Bush, represents CTIA (formerly known as the Cellular Telephone Industries Association) and said in an email that the Berkeley ordinance was “alarmist” and that it “violates the most fundamental principles of the First Amendment.”

In its lawsuit, the trade group said there was no safety concern “no matter how the phone is worn.”

Many doctors and scientists tend to agree. “X-rays, which emit ionizing radiation, are known to cause adverse biological effects at high doses including cancer,” said Jerrold T. Bushberg, a medical physicist and a professor of radiology and radiation oncology at the University of California, Davis. Cellphones, which emit non-ionizing radiation, do not, he said.

Speaking for himself and as a representative of the American Association of Physicists in Medicine, Bushberg said that possible connections between cellphones and cancer have been studied exhaustively. “We’ve been looking for signs of adverse effects at low levels for over 50 years without success,” he said. “We can’t say it’s impossible, but if there is a risk it would be very, very low, or we would have seen an increase in brain cancers.”

If cellphones were carcinogenic, Bushberg said, researchers would have seen an increase in brain cancer in Scandinavian countries, where cellphones have been used longer and where, because of socialized medicine, excellent cancer registries exist. That has not happened, he said.

At the heart of the debate is “simply one word: radiation,” said Robert Cahn, a senior scientist at the Lawrence Berkeley National Laboratory. “Just because cellphones emit radiation doesn’t make them dangerous,” he said.

Other devices that emit low-energy radio frequency radiation and that have not proved harmful include baby monitors, garage door openers, wireless routers and smart meters.

Nevertheless, Berkeley has a habit of passing first-in-the-nation laws that seem radical but are promptly copied by other municipalities. The city has led the way on a variety of initiatives creating smoking bans, a sanctuary for immigrants in the country illegally, a Styrofoam ban and health benefits for domestic partners. So if Berkeley succeeds in its fight to warn people about cellphones, can Cambridge, Massachusetts, and other cities be far behind?

“If you can get it passed in Berkeley, you have a beginning,” said Susan Wengraf, a City Council member. “If you can’t, forget it, or come back three years later.”

On the streets of Berkeley, reviews for the ordinance were mixed. “Labeling things that have a potential threat is always good,” said Benjamin Fahrer, a farmer who said he creates “urban agriculture on rooftops.” He likened the new law to notifying the public about secondhand smoke and genetically modified foods.

Bill Doran, an engineer from Pasadena who had his cellphone out while waiting in line for ice cream, said, “I’m a little skeptical about cellphones causing harm.” He was more concerned “that I’m not able to get reception here.”