I have a question about how to present numbers in the title of a chapter when I am using APA style.
Answer
APA does have rules about how numbers are presented in-text, i.e. numerical form vs. letters.
However, I think your case is different since the number is part of a title. I would respect the original title. If a book's title was Trench warfare in World War One, you would not arbitrarily change it to Trench warfare in World War 1 when discussing it.
On pp. 104-106 of the Publication Manual of the American Psychological Association, 6th edition, the authors discuss the use of italics in-text. An entire book title would be italicized, but there is no example of italicizing the title of a book chapter. Likewise, in your references, the book title is italicized but not the chapter title. This make me think you would not do so for this.
An example then might be:
White, in the chapter Case #9 of his book, Crazed Australian Shepherds I have known, describes his adventures with a red merle, only described as Case #9, that had a taste for entire pans of lasagna.
I suppose we could spend some time thinking about if there is a difference between the chapter title, Case #9 and referring to Case #9 when it is not the chapter title, and should one be capitalized and the other not, but then people might start to wonder as to whether or not we have a life. I think for consistencies sake, and not to confuse your reader, I would treat them both the same.
Unless, in the text of the chapter, Case #9, the author uses "case #9" when referring to the case, I would then follow the author's lead.