Assistant Police Chief Noble Wray said Thursday on CBS News' The Early Show that police only had a brief interview with Seiler after she was found. They planned to ask more questions Thursday.
"We're going to see what we can get from the crime scene," he told co-anchor Harry Smith. "Then number two, in the coming hours, we will be interviewing Audrey in more detail. And then number three, hopefully there will be some witnesses that will step forward that we can get more information and more detail from."
The 20-year-old's parents were always confident that the University of Wisconsin student would be found after her baffling disappearance from her off-campus apartment last weekend.
"Audrey is doing well. She's happy to be back," said her father, Keith Seiler. "Needless to say she's thrilled to be home again with her family and friends."
University Provost Peter Spear expressed "profound relief and joy" at Audrey's recovery on the school's Web site.
Police are searching for a white male in his late 20s or early 30s, approximately six feet tall, wearing a black sweatshirt, jeans and a black cap, and possibly armed with a gun as well as a knife, reports CBS News Early Show National Correspondent Jon Frankel.
"Audrey reports that she was abducted at knife point," said Wray.
Officer Shannon Blackamore said Seiler did not know the abductor. He also said there was an indication or threat of a gun, though Seiler never saw the weapon.
"Audrey reports she was not free to leave and was not injured," Blackamore said.
Seiler was treated at a hospital and released after being there less than six hours. Dr. Philip Schultz said Seiler was cold and dehydrated and had muscle aches as a result of being confined.
Other than that, "according to the doctors, she was in good condition," Wray told CBS News. "When we talked to her yesterday, she appeared to be in good physical condition."
Her discovery capped an intense search in which dozens of volunteers from Seiler's hometown slogged through marshes and woods around campus and investigators scoured phone records and apartments for any clue into the disappearance. Police used dogs, planes and boats in the search.
Officer Larry Kamholz said Seiler was found after an employee at a nearby office building called police to report what she thought was a body in the marsh less than two miles from Seiler's off-campus apartment.
Officers with weapons drawn searched the heavy brush, and a helicopter with heat sensors was brought in to aid the search.
Rejoicing residents took to the streets to tear down missing-person posters in Seiler's hometown of Rockford, Minn., a small town about 30 miles west of Minneapolis.
"Right now it's just an unbelievable feeling," said Roman Pierskalla, principal of the high school in Rockford. "Today, the prayers of everyone in the Rockford community have been answered."
Later, a candlelight vigil turned into a celebration; a local Domino's sent free pizzas and the Rockford Fire Department brought a ladder truck that hoisted an American flag.
Seiler was last seen on a surveillance tape from her apartment building early Saturday. She apparently left without her car or any personal belongings, and her door was left open.
Seiler was involved in another mysterious incident Feb. 1, when she was struck from behind by an unknown assailant and knocked unconscious. Police say she was then moved about a block from where she was attacked but was not sexually assaulted or robbed, authorities said.
Audrey's uncle, Scott Charlesworth-Seiler, said at the time of the earlier attack, his niece had no idea who may have wanted to harm her and believed the attack was random.
"Audrey was worried after having been attacked and, as a result, was more careful to walk with friends and make sure she was safe," he said.
Police are unsure if there was any connection between the Feb. 1 attack and Seiler's disappearance, which was a shock to people in Rockford, even though it happened so far away.
"A lot of people out here sleep with their doors open," said Nate Rivera, a supervisor at the Phillips 66 Quick Shop. "That's probably not going to happen much longer, even though it happened in Wisconsin."
For many in the Midwest, the Seiler case brings back the trauma of the disappearance of another Minnesotan: University of North Dakota student Dru Sjodin, kidnapped last November from a shopping mall in Grand Forks, North Dakota.
Police have said that they believe Sjodin, 22, of Pequot Lakes, Minn., is dead. Alfonso Rodriguez Jr., 51, of Crookston, Minn., was charged with her kidnapping charges after police said traces of Sjodin's DNA were found in blood in his car.
Police also found one of Sjodin's shoes, elsewhere, a few days after her disappearance. But her body has not been found.