"I do not need it" is wrong. Is this because for an inanimate object, you would use "to" instead of "ji"?
I think it is not about animate/inanimate object, "ji" simply suggest that it will be feminine noun, and it doesn't matter if it is animate or not (you only distinguish that with masculine nouns), so you would say "Já ji nepotřebuju." when talking about both about a girl (dívka) and a pencil (tužka). You would use "Já to nepotřebuju." (I don't need it.") when talking about neuter nouns.