ATON ROUGE, La., Jan. 3 — Recently, the police asked Shannon F. Kohler if they could swab the inside of his mouth to analyze his DNA. It was a request they made of 800 men in southern Louisiana as they searched for the serial killer who has slain four young women, leaving behind genetic material in each case.

It was his choice, Mr. Kohler said the officers told him, but if he refused, they would get a court order and that would get in the newspapers and then everyone would know he was not cooperating. The approach was heavy-handed and foolish, he said, especially since he has feet much bigger than the prints left by the killer and had phone bills that show he was at home when the murders took place.

The questions Mr. Kohler is raising about DNA testing are also being asked by lawyers and other experts around the country who say the growing use of DNA dragnets like the one here, already one of the largest in American history, is troubling.

The tests, supposedly voluntary, can still be coercive, critics say, not only harassing innocent people but also potentially violating suspects' constitutional protections against compelled self-incrimination and unreasonable search and seizure. Future prosecutions could be undermined, some legal scholars, defense lawyers and even some prosecutors say. Some question whether the dragnets' limited success justifies the effort and expense. And even those who endorse the idea of DNA sweeps argue over whether — and why — the government should keep on file the genetic profiles of those who are proved to be innocent.

The tests trouble some for the very reason that police find them attractive: they offer the most incontrovertible proof of identity.

The idea for a DNA dragnet — sampling people who are not suspects but merely live or work near a crime scene — emerged in Britain. In 1987, the police tested 4,000 men in Leicestershire before the rapist and killer of two girls was caught after he got another man to take the DNA test for him. One of the first dragnets in which DNA actually identified a killer was in Wales; a neighbor of a slain rape victim was caught in a DNA sweep of 2,000 men.

By 1998, dragnets had taken hold in northern Germany, where 16,400 people were tested — believed to be the most yet — before a mechanic was matched to a rape-murder.

In the United States, mass screenings have had less success and stirred up far more controversy. In 1994 and 1995, the Metro-Dade police in the Miami suburbs took more than 2,000 DNA samples in search of the strangler of six prostitutes, and initially focused on three possible matches before each man was ruled out. Still, the killer was caught only after neighbors found a prostitute bound and gagged in his apartment while he appeared in court on an unrelated robbery charge.

In 1998, the police in Prince George's County, Md., sought DNA samples from 400 male workers at a county hospital where an administrator had been raped and strangled. Union members complained that the police were bullying employees into agreeing and were singling out maintenance workers. No match was made, and the killing remains unsolved.

The chief of the county's police force at the time, John Farrell, defended the DNA tests to USA Today in 1998 as analogous to fingerprinting everyone who worked or shopped in a store that was burglarized, to eliminate potential suspects as well as to catch the criminal.

But mass fingerprint gathering is all but unheard of in criminal cases, said James Alan Fox, a professor of criminal justice at Northeastern University, precisely because of the probability that a print obtained from a crime scene will turn out to be someone's other than the criminal's.

DNA is different, Professor Fox said, which accounts for its allure: "If you have a rape and murder, and there's semen recovered, it's highly unlikely that it was innocently left there."

Not surprisingly, DNA screenings have been much more successful, if no less provocative, when the police have narrowed their focus to smaller groups — generally those with opportunity, if not motive.

In Lawrence, Mass., in 1999, the police drew blood from 32 men at a nursing home where a resident had been raped and impregnated. A nurse's aide was linked to the crime and pleaded guilty. In Los Angeles that year, detectives who reopened the case of a 1985 killing of a sheriff's deputy set about sampling 165 potential suspects. They had finished 12 when a former colleague of the victim refused to comply; detectives won a court order, matched his DNA to the crime, and were about to arrest him when he killed himself.

Professor Fox, an expert on serial killers who wrote a book on the murders of five University of Florida students in Gainesville in 1990, said investigators in that case, with whom he worked as a consultant, checked the DNA of hundreds of people identified as possible suspects, often surreptitiously.

"We'd follow people as they went through Burger King, and pick up a straw they used, for saliva," he said. "We'd go through their trash on the sidewalk. Not everybody we got DNA on even knew it."

The police were far less quiet about their DNA testing in Ann Arbor, Mich., in 1994, after 13 women in a predominantly white community were raped by a black man. Investigators identified more than 700 suspects and took 160 DNA samples from black men, relying on tips that often proved specious.

The strategy caused a racial furor, with blacks saying they were being randomly singled out, and the rapist was caught only after a cab driver spotted him with blood on his clothes.

Some legal experts are now calling for an even more controversial use of genetic forensics: a national databank of DNA taken from every American at birth, solely for the purpose of criminal identifications.

Michael E. Smith, a University of Wisconsin law professor who led a working group for the National Commission on the Future of DNA Evidence, said such a databank would remove the danger of racial discrimination in DNA testing, as well as the risk that law enforcement agents seeking genetic information would turn to hospitals and medical laboratories, eroding medical privacy rights.

Even better, Professor Smith said, it would make DNA a true deterrent to crime, which it cannot be so long as the DNA databanks contain only information on known criminals and suspects.

The federal government's existing DNA database, by law, includes only material taken from convicted criminals and crime scenes. Increasingly, states including Louisiana and Virginia have authorized the collection of DNA from people arrested for rape, murder and other violent crimes, and in some states even for burglary and lesser charges. The law in most states is much less clear when it comes to the DNA of people merely suspected of a crime but not charged. Yet it is being tested.

In New York City, for example, the medical examiner's office maintains a citywide database of DNA obtained from crime scenes and from suspects in major crimes, either with their consent or with a warrant, said Dr. Howard J. Baum, deputy director of forensic biology.

But in November, a defendant in a Brooklyn rape case who was compelled to give a DNA blood sample won a court order barring the medical examiner from placing it in the citywide DNA database, known to medical examiners as Linkage. The defendant, Carlos Rodriguez, argued that a 1994 state law preventing DNA test results from being disclosed without the subject's consent also barred officials from entering those results into the city database. Justice John M. Leventhal of the State Supreme Court even wrote that the mere existence of the database might constitute a felony under the 1994 law. The medical examiner's office is appealing the ruling.

Mr. Kohler, the Baton Rouge man who demanded a court order before giving a DNA sample, says he, too, plans to sue to get it, and his genetic information, back from the police.

Mr. Kohler, a 44-year-old welder, said he resented the way the police relied on a pair of sketchy tips and seemingly irrelevant evidence as their probable cause, though it was enough to persuade a local judge to issue a warrant. Mr. Kohler said the police cited his 20-year-old burglary conviction, but not his full pardon and restitution in 1996.

Mr. Kohler said he felt that the police violated the Constitution by leaning on him for the DNA sample.

"These rights are what makes America America, to me," he said, adding that he felt he could afford to protest while many others could not.

"My friends know me, and I know me, and other people really don't matter," he said. "I'm not running a business, and I don't have any kids. So I had the freedom to take a stand and not hurt the people around me."

In the end, Mr. Kohler, alone among 15 people who refused the DNA test, was indeed identified in public court documents, and hours later a local television reporter appeared at his front door. The police called the court filing a good-faith clerical mistake. The DNA test later cleared Mr. Kohler. And the killer is still at large.