MADISON, Wis. -- Extra police patrols continue to blanket Madison's downtown area, as police continue to investigate the slaying of a University of Wisconsin-Madison student who was found dead Wednesday at her apartment near campus.

Brittany Sue Zimmermann, 21, of Marshfield, was found on 500 block of West Doty Street on Wednesday. Her fiancé found the woman's body in the first-floor apartment in a two-flat house that they shared at about 1 p.m. Police said that the fiancé isn't considered a suspect.

An autopsy determined that Zimmermann died of "a complexity of traumatic injuries," but authorities weren't specific.

Meanwhile, officers and detectives have spoken with numerous residents, commuters, business owners and transients in the neighborhood, police said.

They said that received more than 75 tips from Crime Stoppers, many from people reporting that strangers came to their doors or into their homes in recent weeks. Other tips came from downtown residents who said that they saw people going door-to-door, asking for money on the day of Zimmermann's killing.

WISC-TV reported on Thursday that a male intruder confronted a 21-year-old woman living two blocks from the homicide scene. That incident happened shortly before Zimmermann's body was found.

Now, WISC-TV has learned of three other similar reports. Police won't answer specific questions about them, though, so it's unknown if the stranger has been located or even identified.

Valerie Zelinski had just arrived home from work at her apartment in the 800 block of East Johnson on Tuesday when she heard a knock at the door. She said she opened it slightly to find a white man about 40 standing close to it.

"He was really close to the door, and then he took a step closer," Zelinski said of the encounter.

Zelinski said that about 2:30 p.m. Tuesday, the man walked up the steps at her residence, went through an unlocked front door and knocked on her first-floor apartment door.

"He told me the story about having a flat tire and couldn't get a hold of his friends, and then he asked me for $40. And, I said, 'I'm not going give you $40.' (And he said), 'Well then, how bout $20?' So, that's when I shut the door and I locked it,'" Zelinski said.

That story is the same one a white man told another 21-year-old woman on West Washington Avenue Wednesday, after he went through her front door and started to climb the stairs to her bedroom.

Holly Davis' description of the intruder is similar to Zelinski's, who also called the man 'grungy' and reported "salt and pepper hair."

"He had dirty blue jeans on, and a T-shirt, and he was older, probably like 40. But I didn't automatically assume he was homeless," Zelinski said.

She said he didn't appear intoxicated or influenced by drugs. She added that he had "very blue eyes."

WISC-TV has learned that incident was only the first of four sightings of a white man fitting a similar description who offered the exact same story for a flat tire in need of $40.

The first sighting was at Zelinski's on Tuesday afternoon on the 800 block of East Johnson Avenue.

The second was on Bedford Street, one hour before Zimmermann's body was found Wednesday on West Doty St. A person said a man left WORT radio station on Bedford at noon and walked down the 500 block of West Doty, disappearing when he ducked in between some houses or apartments that were either next to or close to Zimmermann's house.

The third sighting occurred two blocks away about 50 minutes later at Holly Davis' apartment on the 500 Block of West Washington Avenue.

And the fourth incident happened at a restaurant on the 600 block of Williamson Street.

"It's really freaky because I always walk around to go places instead of driving, and now I have to think twice about it cause it's scary," Zelinski said.

Zelinski reported her stranger encounter Friday at noon to the police, and she said they wanted a detailed description. She said the man was about 5 feet 9 inches tall and had salt and pepper hair.

Police said they are questioning the transient and homeless, but a homeless advocate warned against any rush to judgment. They worry people will condemn an entire segment of the community as violent, which she said is completely unjustified and unfair.

Lt. Joe Balles said neighbors in the area where Zimmerman was killed are regularly approached by transients asking for money. Balles said that investigators haven't determined a homeless person killed Zimmerman.

City Council President Mike Verveer, who lives in the neighborhood near campus, said that it's possible a transient person simply has information that could be helpful to police.

Madison police said that they don't have a suspect or suspects in the slaying nor a motive. They said that Zimmermann's slaying might have been a random act.

UW To Hold Vigil On Sunday

UW-Madison officials are remembering Zimmermann as a driven student who had a bright career in front of her in the field of public health.

UW officials said that a memorial vigil for Zimmermann has been scheduled for 7:30 p.m. on Sunday on Library Mall. Berquam will lead the ceremony, along with student representatives from Associated Students of Madison, the Wisconsin Union Directorate and the Union Council, according to a UW news release.

A member of the Dane County's Victim Witness unit is working with Zimmermann's family and she will be keeping them posted on developments in the case, WISC-TV reported.

Both SAFEride and SAFEwalk services on the UW-Madison campus continue to be in demand. On Friday night, 22 SAFEwalks were requested -- more than usual but typical of a very busy Friday night.

But there were 110 SAFEride cab rides, which is double the normal amount. Coordinators said that students who have never used the service made up the bulk of the walks and rides.

There will be a neighborhood meeting Saturday afternoon to give downtown residents the latest information and answer any questions they might have about the crime. The meeting will be held at 2 p.m. Saturday at the Capitol Lakes Retirement Community at 333 West Main Street.

Authorities said that anyone with information about Zimmermann's death should contact Crime Stoppers at 608-266-6014.

Stay tuned to WISC-TV and Channel 3000 for continuing coverage.