New Orleans ? With a suspect under arrest in the Louisiana serial killer case, investigators are facing questions about what they are going to do with DNA samples collected from more than 1,000 men as part of a huge genetic dragnet.

Already, one man who was ordered to submit to testing is suing to have his DNA removed from police files. Legal experts said the case could help determine where the line is drawn between the interests of a criminal investigation and personal privacy.

“Our constitutional protections are supposed to protect us from this type of behavior because, without that, we basically live in a police state,” said Shannon Kohler, a Baton Rouge welder whose lawsuit contends police lacked sufficient grounds to take his genetic information while looking for the man who killed five women in southern Louisiana since 2001.

Mary Ann Godawa, spokeswoman for the task force that led the hunt, said Friday that officials had not decided what to do with the DNA bank.

While DNA dragnets have taken place throughout the country, the American Civil Liberties Union is aware of only one other person to successfully sue for the return of his genetic sample. That was Blair Shelton, who gave a sample in 1995 during an investigation into a series of rapes in Ann Arbor, Mich.

The ACLU is not involved in Kohler’s case but supports his effort, said Barry Steinhardt, a privacy rights specialist with the ACLU’s national office in New York.

“All those samples should be destroyed,” Steinhardt said. “These are people who are, in a sense, certifiably innocent, and there’s no justification for holding on to their samples.”

Kohler said he received unjust notoriety when police went public with his refusal to voluntarily give his DNA. Ultimately a judge ordered him to supply a mouth swab. It turned out not to match genetic evidence from the killer’s victims.

Derrick Todd Lee was arrested in the five slayings this week.