What to do with a dead Cat
If necessary, use some old cloth, an old towel or gloves to handle the cat. Wash your hands afterwards. Notify the owner(s); otherwise, they will look for their cat and wonder what happened to it for years (sometimes the cat carries a tag with a phone number – look for that). If the owners are unknown, take the cat to the nearest veterinary. The veterinary will scan for microchips and similar to locate the owners etc.
What to do when your cat dies at home
If you are the owner of the cat, you can bury or cremate (cremation individually or with other animals at a cost). In general, in most countries you are allowed to put a small animal such as a cat in the trash, if you put it in a bag first. But remember, a cat that has been a friend deserves to be buried. You can bury it on your own property or at a pet cemetery. A veterinarian can help you with arranging cremation.
What to do if you find a dead cat
Unless it is obvious that the cat is dead – the first thing to do is to check for signs of life. If the cat’s eyes are closed, the cat may be alive, as closed eyes requires some muscle control. If the eyes are open, you can use the flashlight on your cellphone to check if the cat’s pupils retract in response to the light – suggesting that the cat is alive. If the cat is alive, take it to the nearest veterinary (unless the cat has a collar with phone-number to call). If you have deduced that the cat is dead, you should still take it to the nearest veterinary (unless the cat has a collar with phone-number to call). The veterinary will scan for microchips and similar to locate the owners etc. Otherwise, owners will look for their cat and wonder what happened to it for years.
In sum: Take it to the nearest veterinary (unless the cat has a collar with a phone number to call).
Can I put my dead cat in the trash?
The rules may differ between countries, but in general you are allowed to put it in the trash, if you put it in a bag first.