I know that when at least one new permission is added, the app will not be auto-updated. The user has to manually update it. You will have "Manual Update" when the app's permissions have changed.
What about removing a permission ?
My current app version N is released. In the next release, one permission is removed.
Will the users of version N get an automatic update ?
Whenever you see an app that requires manual updates, it’s because the app requires additional permissions. Usually, the app’s developers added a new feature that requires a new permission.
http://www.makeuseof.com/tag/app-permissions-work-care-android/
So removing a permission will not cause manual update.