見分け方の解説として,こう書いてあります。
Take away the first subject and see if 'I' still sounds right.
If it doesn't, you can be confident that you should be saying "me".
ルール:
How to decide: Look at the clause that is introduced by which or that.
①If the clause can be dropped without losing the point of the sentence, use which.
②If the clause is essential to the sentence, use that.
具体的にどういうことかというと,
1. I don't like a salad that has too much dressing on it.
2. I don't like a salad which has too much dressing on it.