In this case, the active verb would be "respek" not "perlu."
So, "I don'tneed to respect you" would be something like "Saya tidak perlu merespekkan anda." However, I dont think "respek" would be conjugated this way, it sounds weird. But you get the idea.
Yeah it gets weird because "respek" is an abnormal verb, a transliteration of the English word. So its functions become a bit muddy. I would prefer they had introduced the verb "hormat" instead.