Cicada shell

Cicada Shells are a "bug" that can be caught in. It is technically just the skin left behind by a Cicada Nymph, it's the only "bug" in the game that isn't alive. Cicada Shells can be found on trees and the player can run or walk past these and it will stay. The only way to make it disappear from the tree is if you shake the tree or hit it with an axe, then it will drop on the ground and disappear.

Donating to the Museum
As with all insects in the Animal Crossing series, Cicada Shells can be donated to the Museum followed by a small talk by Blathers, the curator.

In New Leaf
"Cicada larvae emerge from the ground in the evening and molt on trees, leaving behind empty shells. It's possible to find out the species of cicadas just by looking at these shells. Collecting the shells will tell you how many and what kind of cicadas inhabit a certain area."

It can be found in the top section of the upper right room in the bug habitat of the museum, with the other cicadas.