Questions were also surfacing about how much the school knew, and should have known, about Huguely's history.
Love's in a pool of blood early Monday morning in her off-campus apartment by her roommate and the roommate's boyfriend.
Huguely was arrested hours later and charged with first-degree murder.
Love and Huguely, both 22, were due to graduate later this month.
In court documents, police say Huguely admitted to them that he kicked in Love's bedroom door, shook her, and that her head repeatedly hit the wall.
His attorney, Francis Lawrence, says Love's death was an accident.
On "The Early Show on Saturday Morning", CBS News Correspondent Whit Johnson said authorities are trying to learn whether there were any "previous incidents of domestic violence between the couple. They have no documented reports, but they're looking in to several things.
"One report is that the couple actually had to be separated at a bar the night before Love's body was found" due to a heated argument.
"In 2008," Johnson continued, Huguely "had a run-in with a Lexington, Va. police officer, a female officer who felt so threatened she had to use a Taser to take him into custody. He was charged with resisting arrest and public intoxication."
In addition, Johnson points out, "Some former lacrosse players have come out and said that last year, he actually had a fight with one of his teammates."
U.Va. President John Casteen and the school's athletic director, Craig Littlepage, say they didn't know about the arrest and question why they were never told.
Casteen is scheduled to meet privately next week with Virginia Gov. Bob McDonnell. Casteen is pushing to require police to tell schools about off-campus arrests of their students.
But on "The Early Show on Saturday Morning," attorney Wendy Murphy said, "The University of Virginia -- I don't think this has been made public yet -- has a notorious reputation for being not very effective at dealing with violence against women on campus. I have a case involving the University of Virginia right now in terms of their systemic inadequacies in addressing violence against women on campus."
Murphy cautioned parents that, "If you've got a kid in college, it's very important to check out what the policies are at the university in terms of how they handle dating violence and sexual violence, because it's a huge problem on campuses across the country. … So check out what the university policies and procedures are. If your daughter is in danger because the university doesn't have the right rules in place, parents have a need to know."