ARDEN CITY, N.Y., Sept. 26 — A new Web site displaying color photographs, market values and other property data for every home and business in Nassau County is proving to be extremely popular — and equally unpopular.

Critics are demanding that the site be censored or even shut down. Calling it an invasion of privacy, they cite fears that the information it contains could be misused by gossips, burglars, stalkers, kidnappers, rapists and murderers.

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Curious electronic visitors have downloaded millions of pages since Sept. 9, when Nassau put the data online to show the owners of 400,000 properties the results of the first countywide reassessment since 1938.

"We have literally been inundated with letters and calls from people who are extremely disturbed," said the Nassau County Legislature's presiding officer, Judith A. Jacobs, a Democrat. "For the comfort level of the residents, this cannot continue."

Ideally, the Web site should be shut down, Ms. Jacobs said. Short of that, she has proposed limits allowing owners to have their Web files deleted, giving pass codes that allow only owners to review their files, and removing the photographs and property maps, which show the outlines of each building.

Defenders of the Web site (www.mynassauproperty.com) say that everything on it has always been freely available to the public at government offices. Similar Web sites of assessment records have been created by many other localities across the nation.

Nassau's official in charge is Charles O'Shea, a Republican elected as chairman of the Board of Assessors. "The feedback from residents has been overwhelmingly positive," Mr. O'Shea said. Owners find it easy to check the accuracy of their records and compare their new assessments with the values of similar properties, he said.

"There are no plans to take down this Web site," Mr. O'Shea said. "We live in the brave new world of the Internet." But if a rising chorus of legislators opposes it, he added, "I will obviously pay attention."

Mr. O'Shea has already made concessions. The original site enabled searches by owners' names. When law enforcement groups objected, saying their members would be vulnerable to retaliation from criminals, he barred name searches. Today, facing rising criticism, Mr. O'Shea ordered the deletion of the owner's name listed for each property "as a result of security concerns expressed."

That did not satisfy the official who first attacked the site, Craig M. Johnson, a Democratic county legislator. "That's a good first step," Mr. Johnson said, "but let's finish the job and shut the thing down."

No one on either side of the debate has produced any example of assessment records being abused, in Nassau or elsewhere. "As a father of children," Mr. O'Shea said, "I can understand no one wants it to happen once."

Elsewhere in the country, one murderer used motor vehicle records to track his victim and another used Social Security data, said Chris J. Hoofnagle, counsel to the Electronic Privacy Information Center, a nonprofit group in Washington that advocates limits.

Robert J. Freeman, the director of the Committee on Open Government, the state agency that promotes access to public records, said assessments were a classic example of "the need for privacy being outweighed by the need to know whether the government is treating us fairly" in its taxes. But, he added, "The second question is the wisdom of putting it up on a Web site for the whole world to see."

Mr. Johnson said: "It's all about making it so easy. With a computer, you just don't know who's getting the information. You know, there are computers in prison, and all you need to do is click."