Nicholas Roecker apparently was battling depression when high school friend Kayla Koranda went to visit him Monday afternoon at his home outside Rochester, officials said.
Now both college freshmen are dead in what authorities believe was a murder-suicide.
"The depth of their relationship is still not known at this time," the Olmsted County Sheriff's Office said in a statement. "However, it is believed that they were just friends."
Sheriff David Mueller said his investigators believe that Roecker is the one who fired the fatal shots from a handgun, which was recovered at the scene.
Koranda and Roecker had been communicating earlier in the day, and "we know from family that the woman was just going to visit him due to his depression or that sort of thing," Mueller added.
"We're still waiting to see if we can get into cellphones and additional information that may be available about what motive there was," he said. "We don't know a lot of what led up to what happened at the scene."
Roecker, 19, attended the University of Minnesota Duluth. Koranda, 18, attended the University of Minnesota's Twin Cities campus.
Roecker was a science and engineering student living at UMD's Griggs Hall. Koranda was a liberal arts student residing at Middlebrook Hall.