@preetig
In my experience, the coding or scripting of the API tests was good enough for the documentation. If better documentation is required, add detailed comments into your test code. In addition, your test code should be stored in a repository where again additional information can be stored.
These scripts, and hence your APIs, should be linked to functionality that allows you to gauge coverage if you are interested.
As with the age-old questions around test cases, what is the purpose of your documentation?