My young cat died very suddenly yesterday. Did my dog do it?

It was probably just a sad coincidence. I cannot think of a way that a dog could kill the cat without injuring the cat in a noticeable way. The cat could die from internal things, but for it to be that hurt there would also be external signs. The dog may have helped the cat get into something by opening it, but if you see no signs of that either chances are your cat's death had nothing to do with the dog. If you really want to know, talk to your vet and see if you can have the cat examined. This may be expensive, and it won't bring him back.