Thank you all! I called Animal Control and got an answer (Thanks for the suggestion!)
She has a duty to look over her hens and if my dogs end up injuring and/or killing her animals on our fenced property, then we are not liable. It is slightly different if it is unfenced property due to Colorado's open range / fence law.
Excellent! Don't forget to document this conversation and make lots of notes about it. Animal control would be the final authority if your neighbors try anything.
I'm glad you got an answer. I would think that since the bird came onto your property and died, it could have been anything that killed it, not necessarily your dog. I have several game cameras on my property and have seen dogs and cats on my property. I have asked some of the closer neighbors if they know who they belong to but no one seemed to know but have seen them roaming too. We are rural on a dead end road. Now I am going to do some research and see how different places handle something like this. Just curious... Good luck...