I would add a meta box to the books custom post type, containing an input field with autocompletion, to select the author from the existing authors.
You can also use a standard dropdown-field, but it gets crowded if you have a lot of authors.
On the save_post action, add a meta_data field with the ID of the author to the book:
update_post_meta($book_id, '_book_author', $author_id, $prev_value);
Also, to have a good overview, I would add a metabox to the author custom post type, containing all the books assigned to this author.
You can either query them directly (SELECT 'post_id' FROM wp_postmeta WHERE meta_value="$author_id" AND meta_key = '_book_author'), and outupt a list with the links to the edit.php of the corresponding book, or you could save the meta_data for the books as well (when saving the book), something like:
add_post_meta( $author_id, '_books_by_this_author', $book_id );
If you choose the second version, be sure to handle the redundant data right – you could end up with a lot of dead links if you do not delete the post_meta when deleting or updating a book.
I assume you know how to add meta_boxes and the hook to the save_post action?
if not, check out this article
I did not explain everything in detail here – as well as I did not write the query in the best WordPress way, I just wanted to give you my input on how to solve the problem, not to explain it from scrath. if you need more help on that, please let me know.