Dodds called the incident "inappropriate," but noted it was also something that happened between consenting adults.
Dodds said the university's legal office looked in the matter.
"We have high standards for behavior and expect our staff and coaches to adhere to them in all aspects of their lives," Dodds said. "I believe the appropriate discipline was taken in this case."
Texas women's track coach Bev Kearney resigned in January as the school was in the process of firing her for having a relationship with one of her athletes in 2002. In 2011, the university paid $400,000 to a former administrative assistant who complained of sexual harassment by Cleve Bryant, a former top athletic official in the football program.