How to retrieve Office365 Planner Plans, Tasks and Buckets in console application using CSOM C# or using Powershell ?
As it stands now, you can't use CSOM to access Planner, but you can use the Graph API: https://developer.microsoft.com/en-us/graph/
This functionality is currently in beta in the Office Graph. See this page for documentation on retrieving tasks. For other capabilities, see the left nav on that page, scroll down to the beta section, and there's a category for "planner tasks", as well as "plans".