MOSCOW - A University of Idaho graduate student who was gunned down outside her off-campus residence and a former professor at the Moscow school suspected in her murder may have previously had a relationship, police said Tuesday.

Ernesto A. Bustamante, 31, checked into a Moscow hotel less than an hour after the shooting, police Lt. Dave Lehmitz said. His body was found early Tuesday with a gunshot wound to the head after he apparently took his own life, Lehmitz said.

A warrant had been issued for Bustamante's arrest after officers found Katy Benoit, 22, dead at her Moscow home late Monday. The woman, who is from Boise, was shot multiple times with a .45-caliber handgun outside her home while her roommate was inside, Lehmitz said.

"It appears that the victim and suspect were known to each other and may have had previously a relationship," Lehmitz said.

Bustamante was an assistant professor in the university's Department of Psychology and Communication, earning a base salary of $51,000 a year, when he resigned his position with the school on Friday. He had been with the school since August 2007.

Benoit earned her undergraduate degree in 2010 and started her first year as a graduate student in the psychology department this fall, according to the university.

Classes started on the northern Idaho campus on Monday. A ceremony to mark the start of the academic year was postponed Tuesday.

While police could not confirm the nature of the relationship between the two, UI Dean of Students Bruce Pitman noted there was a university policy that bars faculty members from entering into romantic relationships with students.

Pittman declined to comment on why Bustamante resigned last week.

Authorities named Bustamante as a suspect shortly after the shooting and served a search warrant at the University Inn Best Western, where police found Bustamante's car. The body was found inside his hotel room.

"We are both shocked and saddened by these events. Our heartfelt sympathy goes to the victim's family and friends," the university said in a statement.

Bustamante has no prior criminal record in Idaho. Court documents show a few traffic violations in Latah County, where the university is based.