Dress Gray (1986)

"Nothing will tarnish the name of U.S. Grant Military Academy. Not even murder."

When a cadet at a military academy is found dead, the assumption is it was an accident. But the autopsy reveals that's not the case and that he's a homosexual and the last person he was with someone before he died and that someone is an academy upperclassman. The commandant wanting to protect the academy's good name tries to keep it quiet and hopefully no one will care about it. But the cadet comes from a prominent family and his father knows it couldn't have been an accident. And his sister knows one of the upper class men who knew his brother. And he learns the truth of her brother's death when he spoke to the academy doctor. Later when the commandant learns of this he orders the man brought to him and tells him to forget what he learned. But he sets out to find out the truth. At the same time the commandant gets some info that might implicate him.