 At no point in this movie is the line "Me Tarzan, you Jane" spoken.  When Jane and Tarzan meet, it is she who initiates the verbal  exchange, repeatedly indicating herself and giving her name until he  repeats it. She then points to him, indicating that she wants to  know if theres a word for who he is as "Jane" is the word for who  she is, until eventually he understands and says, "Tarzan."