Examine the suspended object visually. Upon close visual inspection, you should be able to tell if it is just a curled leaf. Moth and butterfly cocoons hang from branches or appear to rest on a leaf, attached to the surface through silk spun by the caterpillar.
Lift the leaf or branch gently to examine the object further. Structures that appear to have a wrapping of a thin silk material are cocoons or chrysalises. The chrysalis of some butterflies, such as the monarch butterfly, appears to be see-through, in which you can sometimes view the wings of the butterfly through the underside of the chrysalis. Moth caterpillars, such as bagworms, tend to camouflage their cocoons by incorporating parts of the leaves or branches into the structures.
Touch the structure lightly. If it is hard and tough-feeling, it is generally a butterfly chrysalis. If the structure feels soft to the touch, it is likely to be a moth's protective cocoon.
Inspect the area around a cocoon for any other cocoons. Sometimes, caterpillars will create a little colony of cocoons, resting inside a large silk-spun structure in trees. If one of these is close by, the odds of your object being a cocoon are good.