Case refers to a specific type of inflection of a word when used in certain syntactic environments. So for example, the words they and them are nomally thought of as being instantiations of the same word. Which one of them we find in a particular sentence depends on their grammatical relations within that sentence. We call the first ɴᴏᴍɪɴᴀᴛɪᴠᴇ and the second ᴀᴄᴄᴜsᴀᴛɪᴠᴇ, largely by virtue of the fact that the first inflection is associated with subjects and the latter one with objects.
English common nouns, however, do not inflect for case—although noun phrases can take a genitive clitic. When people talk about the case of common nouns (as opposed to pronouns) in English, they talk about them being ᴘʟᴀɪɴ ᴄᴀsᴇ. However, what this really means is that they are not a single word noun phrase with the genitive clitic 'S attached.
People who have studied languages like Latin sometimes try to talk about the case of uninflected nouns when talking about languages that don't have case. What they are doing, though, is confusing the grammatical—or semantic—relations of a word with its (non-existent) case. So they relate the gramatical relations of a word with the case it would have in a language like Latin and try to project that case onto the caseless word.
People also, more reasonably perhaps, try to extend the case of a noun within a noun phrase to the case that it would have if it were a pronoun. So they might say (I know I myself have done this in the past, when I was fuzzier than I try to be today), that John in John ate the elephant is 'nominative' because a pronoun in subject position would be nominative. This is not a great idea though, because it makes it sound as if nouns actually have some kind of property, 'case', which they don't actually have. We are in reality just describing the grammatical relations when we try and pull tricks like this (saying that John is nominative just means that John is the subject, nothing more).
Furthermore we cannot pull this kind of stunt with the Original Poster's example, because pronouns cannot funtcion as the head of NP's with possessive determiners. In other words we cannot replace book with a pronoun here and retain the same meaning (although we could play word games where we played with citations of a pronoun).
In conclusion, in the Original Poster's example the word book could be described as 'plain case' if one wanted to emphasise that it had no genitive clitic attached. However, it has no case in any meaningful sense of the term.