Authorities say there have been no signs of forced entry where the victims were murdered or abducted. That has led to speculation the murderer could be anyone from a delivery man to a police officer - a man using a uniform to get to the women.
State Rep. Yvonne Welch said taking cheek scrapings or saliva swabs for DNA testing from the police could at least clear law enforcement of suspicion, if it doesn't catch the murderer. DNA linked one man to the five murdered women.
"Women have told me they're afraid to stop when it's a police officer. The women ought to be able to feel safe that the police are the ones that are protecting them," Welch said.
But police, the governor and the mother of one of the victims said such a step could divert time from more important investigative work in the case.
"I don't know if it's a waste of time. I don't want to tie up resources on speculation," said Police Chief Pat Englade. "We don't want to get into the business of randomly swabbing everybody in Baton Rouge."
Authorities have embarked on a massive DNA dragnet to find the killer of the five known victims - four in Baton Rouge and one in Lafayette.
More than 1,000 men have been swabbed, picked to "volunteer" for the tests based on tips or information generated in the investigation. Defense attorneys in Baton Rouge have said some of their clients have agreed to the testing to avoid speculation they could be the killer.
Welch wants as many men as possible swabbed. She said she's paying to have DNA samples taken from her husband and son to clear them although no one has suggested they are involved.
Englade said police need probable cause to force someone to submit. He said some police officers were already tested because of specific tips. However, testing thousands of officers could distract the crime lab, he said.
Family members of the victims are split on the issue.
Ann Pace, whose daughter, Charlotte Murray Pace, was the killer's second victim, said she thought some law enforcement officers closely connected to the case should be tested. But she didn't agree with across-the-board swabbing.
Sterling Colomb, whose sister Trineisha Dene Colomb was the killer's fourth victim, said he believed all police should be tested.
"Right now, everyone thinks it's a cop. I think it could eliminate that," he said. "You never know. Nothing hurts. It could take time, but it could catch him."
Gov. Mike Foster has said no expense is too great in tracking the killer, but he is not pushing for tests on police.
"No one's had any indication this guy's been posing as a policeman or that policemen are involved," Foster said on his radio show.
Rep. Jack Smith reminded the head of the Louisiana State Police at a legislative hearing that a serial rapist in Lafayette who struck between 1986 and 1997 was a 20-year police veteran.
"I was a police officer for a number of years and unfortunately, as hard as we try through the interview process, every once in a while somebody slips through who shouldn't have gotten there," Smith said. "We might have a bad apple out there."
By Melinda Deslatte