Mourners hug during Virginia Tech's Day of Remembrance in 2008 honoring the 32 people killed in a massacre a year earlier.
The state and attorneys representing two victims of the 2007 Virginia Tech massacre are seeking a hearing before the state Supreme Court.
They appeared Tuesday before a three-judge panel to make the case that the full court take their appeal.
An attorney for the parents argued Tuesday that Tech's President Charles Steger should be tried for his actions on April 16, 2007, while the state is seeking a reversal of a jury's verdict for the families in a wrongful death lawsuit one year ago.
The justices will decide whether the full state Supreme Court should hear their appeals. That decision is expected in four to six weeks.
The hearing stemmed from a successful suit against the state brought by two families who say their daughters could have survived if the university had alerted the campus earlier of the first killings on the Blacksburg campus by a student gunman.
Both sides are appealing various aspects of the case.
In June 2012, a judge upheld a jury's negligence finding against the state, but the damages were sharply reduced. Neither Tech nor Steger was named in the lawsuit.
Thirty-three people died during shooting rampage, including the gunman, who killed himself.