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