While the app is only available on the US App Store currently, the equivalent website seems to work in all territories and on non-Apple devices, though the support contact details remain American.
Apple’s press release on the service states:
“The COVID-19 app and website allow users to answer a series of questions around risk factors, recent exposure and symptoms for themselves or a loved one. In turn, they will receive CDC recommendations on next steps, including guidance on social distancing and self-isolating, how to closely monitor symptoms, whether or not a test is recommended at this time, and when to contact a medical provider. This new screening tool is designed to be a resource for individuals and does not replace instructions from healthcare providers or guidance from state and local health authorities.”
Apple also said that at no point does the app or site require you to sign in with an Apple ID, and “users’ individual responses will not be sent to Apple or any government organization.”
The service adds to each individual country’s own governmental official services following the coronavirus outbreak. Apple’s CDC and White House approved service shows both the influence of the company and the proliferation of iOS devices in the United States in particular.