I am a graduating veterinary student. In most states it is illegal for the veterinarian to euthanize a pet without the owners consent. There are exceptions but a sick kitten dealing with a uri is unlikely to qualify for those instances.

OP, you need to check any and all paperwork that you signed. When designating the shelter as the fiscally responsible party you may have granted the shelter agency over the cat’s health and they may have opted to euthanize over treat because it is a much cheaper option. Even if there is no clause in any contract that designates the shelter as a party able to consent to euthanasia, this may have been a mix up.

If the shelter was paying for all the treatment, the vet may have assumed them to be the owner of the cat. I say that because it is very unlikely that vet would euthanize the cat without consent.

I would say the first step is to contact the vet and request your kittens medical history and request proof that of consent to the euthanasia. They should be able to provide both, but if your pet falls into one of those ‘medical exception