1. Relating to having the quality or character of denying that a thing stated is completely true: The students in class gave contradictory stories about the fight that took place outside on the playground.
2. Pertaining to being inconsistent in itself; containing elements opposed to each other: The people who saw the accident happen gave contradictory accounts to the police, each one saying something different.

Kate gave contradictory statements regarding where she was when the thief stole her money; first, she said she was in the store, then she claimed that she was in the park.