How to form the tag question for sentence like this: She needn't have studied English.
This is an unusual sentence in Present-Day English, because it follows the now old-fashioned use of need as a modal verb in negative and interrogative contexts. As a modal, need is an auxiliary, and should head the tag question:
She needn't have studied English, need she?
Although grammatical, that's so century-before-last that it would startle most hearers. Even people who still use need as a modal would probably recast the sentence using need in the ordinary way, as a chaining verb with do support, to avoid this:
She doesn't need to have studied English, does she?