A complication here is that if the mule is working for the National Park Service, the fact that it is compensated from public funds means that it already be in the public domain. Therefore, you may not need a release.
On the other hand, raising the issue of a release then broaches the subject of whether your usage is commercial, in which case you will need a permit from the National Park Service for commercial photography in a park.
That in turn suggests that you may need a lawyer to sort out the complexities. But then it will be difficult to tell the difference between the lawyer and the mule.
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