Kansas City, Mo ? For the third time in two years, Kansas City police hope they are just a DNA test away from identifying a young girl whose body was found beheaded near a park.

Police said Wednesday they were testing a genetic sample from an incarcerated man who claims he is the father of Brittany Renee Williams of Richmond, Va. Brittany was 7 years old when she was last seen in August 2000.

Investigators believe the girl found April 28, 2001, in Kansas City was between 4 and 6 years old. The brutal killing outraged many in the Kansas City area, and community advocates named the child “Precious Doe.”

Her story, which has been told on “America’s Most Wanted,” helped bring attention to the plight of missing inner-city children, said Alonzo Washington, a community advocate.

“We needed to make Precious Doe as important as JonBenet Ramsey,” he said Wednesday.

Police initially thought they had a match when they received several tips that the computer-generated image of Precious Doe resembled Teekah Lewis, a 2-year-old missing from Tacoma, Wash. But DNA ruled out that connection in June 2001.

Last May, police briefly suspected Precious Doe could be a missing 5-year-old from Miami, Rilya Wilson, but DNA tests ruled out a match in that case as well. Now, the process begins again.

DNA testing of the man who says he is the father of Brittany Renee Williams should be done by the end of next week, police said Wednesday.

“If the testing does not provide a match, since there is some question about whether the sample we have is the biological father of the missing child, investigators will need to decide on the next course of action,” police said in a news release.

Kansas City investigators are working with police in Henrico County, Va., to obtain DNA samples from other relatives of the missing child.

Henrico police said Wednesday they had every reason to believe Brittany is still alive. A picture of Brittany taken close to the time of her disappearance was submitted to the National Center for Missing and Exploited Children three weeks ago. A representative from the center contacted Henrico police about the possibility that Brittany was Precious Doe.

Brittany’s mother gave the girl to another woman — Kim Parker — before dying of AIDS in 1996, authorities said. Brittany also was afflicted with the disease.

It was not immediately known whether tests were performed to determine whether Precious Doe had the disease. The Jackson County medical examiner, Dr. Thomas Young, said Wednesday he could not discuss the case.

In Richmond, police and a social worker testified Parker said she allowed another woman to take Brittany in August 2000 to California. Parker has said she has no way of getting in touch with the woman and Brittany directly, according to police.

Parker was sentenced last week to 20 days in jail for violating a judge’s order to bring Brittany in for a DNA paternity test in October 2001 and for failing to turn the girl over to social workers last month. Parker’s attorney said his client wasn’t capable of fulfilling the order because she doesn’t have the child. Parker is free on bond pending an appeal.

Reached at home Wednesday, Parker said her attorney had advised her not to talk to reporters.

Authorities are eager to learn the identity of Precious Doe — a breakthrough they hope will lead to criminal charges.

“Obviously, we are hoping it works out to be the person. We are being cautious right now,” police spokesman Capt. Rich Lockhart said, adding that investigators have gotten their hopes up before about solving the case. “You get excited about it happening, but then it doesn’t. So then you get let down again.”