What language are you using to make API calls? AdWords API doesn't require you to install any special certificates, but depending on the language and library you are using, you may require to install the certificate for AdWords API site into your machine's trusted certificate store. E.g. mono
requires you to run mozroots command to import the default set of trusted certificates.
Cheers,
Anash P. Oommen,
AdWords API Advisor.