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.