I assume you are talking about API documentation, aimed at the consumers of a library, rather than developer documentation or end-user application documentation.
I don't think there can be such as standard. The requirements of testing are different to those of documentation.
Typically as a user I am concerned with the common case.
As a tester I am concerned with edge cases.
However, developer documentation does have overlap with testing, for example ASSERTIONS can be read by the developer about properties of the program that are not expressed in the code. They also are used by the tester to check the developer hasn't broken these properties.