"She reads me a menu."
Translation:Ella me lee un menú.
Mi (no accent mark) means my. mi libro = my book
Mí (with accent mark) means me after a preposition. para mí = for me
The me in Duo's sentence is the indirect object pronoun that means (to) me.
Both are grammatically correct, but they sound a bit weird, this sentence would be used for something that happens regularly, and by adding a mí you are putting unnecessary emphasis on 'me', like 'me and no-one else', which sounds weird because it's a menu.