Following a golf outing with the Stanley Cup on June 13, 1997, celebrating the Red Wings' Stanley Cup triumph, Konstantinov, along with Russian hockey legend Viacheslav Fetisov and team masseur Sergei Mnatsakanov, hired a limousine to drive them home. The driver, Richard Gnida, whose license was suspended at the time for drunk driving, lost control of the limousine and hit a tree on the median of Woodward Avenue, in Birmingham, Michigan. Konstantinov spent several weeks in a coma. As a result of the limousine crash, Konstantinov suffered from serious head injuries and paralysis while Fetisov escaped with relatively minor injuries and was able to play the following season. Mnatsakanov sustained significant head injuries as well, and spent some time in a coma; he has had a considerably more difficult recovery.