If you order through Life Extension, they'll mail you a blood draw kit if you are able to arrange your own blood draw. It may also be worth browsing the individual test pages on True Health Labs since their FAQ claims they'll mention any state exclusions in each individual test description.
If you're near the border of another state, it could be worth doing a price comparison with the providers mentioned on my individual test pages, since many of them only care about the state in which the blood is drawn. I've been told that if you contact their customer service, they will point you to local service to have it drawn. I think you'll have to pay for the draw services.
That's all I'm aware of for Rhode Island. If I've missed anything, please let me know in the comments so I can improve the page.