How to maintain consistent consequences when child seems to be lying
Our child is 6 years old and is in Kindergarten. Since he was about 3 we have had issues with anger, anxiety, and lashing out with violence (hitting and biting), particularly at school. It had reduced a lot this year, but last week had a flare up, with a couple incidents of hitting and throwing things at another child in short succession.
One consequence we have tried to impose consistently is lack of access to screen time for 24 hours if there is violence at school. I think it's been reasonably successful.
However, today, he told us after school that he didn't hit anyone but someone a lot like him hit someone with a stick, someone basically the same but with a different name. The staff told us that there was an incident where a child hit another child with a stick and it may have been him but they did not see it happen and are not sure exactly what happened.
It sounds like it probably was him, but when he denies it and no one else is reporting that he did it, it feels like we can't reasonably impose the consequence. On the other hand, we don't want to reinforce lying about it either, which seems to be what is happening. What is the best way to respond in a situation like this?