The recent boom in websites offering DNA risk-assessments for diseases has raised some fundamental questions:

Is the science ready?

Will healthy people pay between $1,000 and $2,500 to find out if they might have a higher-than-average risk of suffering a heart attack or developing diabetes or Alzheimer’s?

Is it ethical—or even legal—to offer this service directly to consumers online without a physician?

New York health officials have offered an answer to the last question by issuing letters to at least six companies involved in online genetic testing. The letters warn that offering DNA tests without a physician’s approval is illegal in New York and could lead to fines and jail time.

No one has been arrested or accused of breaking any laws, say officials, but companies that do not heed the warnings could be referred to the New York attorney general’s office.

In California, health officials are investigating consumer complaints about unnamed online genetic-testing companies for potentially violating a similar law that requires the involvement of a doctor in such testing. California has taken no action to date.

Letter recipients in New York include Navigenics and 23andMe, both high-profile companies based in the San Francisco Bay Area. Navigenics is financed by top venture capital firms such as Kleiner Perkins Caufield & Byers, and 23andMe was co-founded by Anne Wojcicki, wife of Google co-founder Sergey Brin.

New York also issued letters to Illumina and Affymetrix, both based in California, which produce the testing platforms used by the websites, though they do not directly offer or market the tests themselves.

New York regulators have not sent a letter to one major online genetic-testing company, deCODEme, based in Reykjavik, Iceland, though this may have been an oversight by the state.

The companies discount the regulators' warnings, saying that their tests are for informational purposes only. "We are not offering medical diagnosis," Navigenics C.E.O. Mari Baker said in an interview with Portfolio.com.

Critics of the companies say that consumers may not understand the distinction. "Telling a person they have Alzheimer’s online is not the best way to deliver this information," geneticist and entrepreneur Jonathan Rothberg said.

Rothberg's former company, 454 Life Sciences, sequenced the entire genome of DNA pioneer James Watson.

Navigenics also offers live genetic counseling service over the phone to its customers—a feature not proffered by its major rivals. Navigenics, which launched its business earlier this month, has put its New York customers on a waiting list while it sorts out the legal issues in the state, according to Forbes.com, which also reported that 23andMe plans to hire doctors to approve tests if the state requires it.

The proliferation of genetic tests in recent months has put pressure on the Food and Drug Administration to investigate regulating testing services that operate with few rules. A recent essay in the New England Journal of Medicine said the services are "premature attempts at popularizing genetic testing," adding that more research is needed to make the tests relevant to individual patients.

For now, online testing companies show no signs of surrendering to these regulatory challenges and every sign of planning to continue to exploit the vacuum between a new, rapidly advancing science and the ability of governments and mainstream medicine to oversee it.

The moves by New York and California to restrain the Wild West of online DNA testing may be merely their first reaction. They're unlikely to be their last.