Your CIP requirements would be the same for a foreign corporation as they would for a U.S. corporation.
Your problem is obtaining, understanding, and perhaps even reading the documents that would be used to verify the company's existence in a foreign company. If a company organized outside of your state, including outside the United States, is doing business in your state it will be required by your state laws to apply for a certificate of authority
to do business in Tennessee.
To an extent, you are relying on the Tennessee Secretary of State's office to act as the gatekeeper and verify the company's existence. The remaining portion of the verification process would depend on your efforts alone and my understanding is that the registration requirements and appropriate documentation vary greatly from one country to the next; i.e. I lack the expertise to generalize about what you might do.