Kyo did not Kill Tohru’s mom. She was hit in a car accident, and he simply did not call for help because he was scared of being seen by her and not being recognized and because he might turn into a cat once she touches her. Kyo and Kyoko (Tohru’s mom) have a relationship that goes way back, even before Tohru and Kyo met. Kyo felt extremely guilty for not preventing what had happened and chose to run away.
When Tohru and Kyoko had just moved into the neighborhood, Kyoko found Kyo slumping on one empty lot looking all bored and frustrated. She started a conversation with him while trying to keep her cool because of how cute Kyo looked. At that time, Kyo was frowning about how Yuki was always so princely and so desirable, while he was an outcast, pitied by everyone, and was blamed for killing his own mother.

Kyoko on the other hand had just found her way back to sanity as she had just lost her husband. She was now a single mother taking care of Tohru, their daughter. Kyo and Kyoko had similar hair colors, and Kyoko found it amusing how someone who was a child like him had the same color of hair as her (she had thought it was permanent, but Kyo said it was natural). During their times together, Kyoko would tell Kyo about Tohru and how she would give her life to protect herself.
Kyo heard all about Tohru even before they met years later. Kyoko even took Kyo to the beach on one of her days off just to play with him. One day, Tohru got lost while she was playing alone, and this scared Kyoko. Kyo happened to pass by, and she asked him for help. Kyo promised he would find Tohru for her, but he looked everywhere and he couldn’t find her. Upon his return, he saw that Tohru had returned to Kyoko wearing a very familiar cap, Yuki’s. Kyo was mad at himself and decided he didn’t want to see Kyoko again.
Years later, they meet again at the traffic light. Kyoko was in a daze and was hit by a vehicle, Kyo had a chance to stop her or prevent the accident, but he was too scared to do so.
Read More: Fruits Basket: Is It Good or Sad?