The Migratory Bird Treaty Act of 1918 was put in place to protect native wildlife from being over-harvested for use in the fashion industry. (Yes, really. Back in the day, you were nobody if you didn't have about 50 feathers AND an entire stuffed bird on your head.) It protects most species of North American birds and makes it illegal to own whole birds, feathers, nests, eggs, or bird parts.
Bird parts that are ok to own include domestic birds, most game birds (with proper permits), and any bird species located outside of North America--assuming its not endangered of course. There are also exceptions made to the law for scientific and religious purposes.
So what is a carcass-happy girl to do?
The best course of action is to take a picture of the bird and leave it where you found it. If you're in the city or suburbs and your bird is going to be removed anyway, go ahead and take it to the nearest bit of wild you can find and leave its body to go back to the earth.
Here is a picture of the last bird someone brought to me, while still fresh. It's currently in a corner of my flower bed where I am letting it naturally decompose. (If you want to share this picture, feel free, but please link back to this blog!)
List of birds protected under the act:
https://www.fws.gov/birds/management/managed-species/migratory-bird-treaty-act-protected-species.php
Further (quick) reading: https://en.wikipedia.org/wiki/Migratory_Bird_Treaty_Act_of_1918
