The official eligibility is :
1.A natural person (i) who is a United States citizen, (ii) who is a permanent resident of the United States of America or any of its possessions or territories, or (iii) whose primary place of domicile is in the United States of America or any of its possessions [Nexus Category 1]
You don't need to be a citizen. If you are a green card holder, or if you can show that the US is your "primary place of domicile", then it will be enough.
In practice, the .us registry operator cannot know whether you are a permanent resident or a temporary resident. They will never try to investigate the domain holders' immigration status, they will never have resources to verify the status of all US domain holders, and the US law will never allow them to examine the status of domain holders. As long as you can provide a valid US address, you will not have any trouble.