Hi,
It depends what you are doing with the helm charts? Mostly people install apps, many install pre-requisites (roles, clusterroles, crds, etc.) apart from the applications (pods).
In case of application, a basic sanity of the application can be planned and could be written as part of tests/<template> in your helm chart wherever possible.
I don't think any other tests are necessary, because post deployment you can follow standard testing process which may include smoke tests, performance tests, penitration/security tests, etc.