To clarify: for many people here, "crime" has the connotation of "true crime", as in the Dewey Decimal classification of 364 (Crime). That is also the way Powell's classifies it. Public library spine labels for fiction genres here use the word "Mystery", not "Crime".
A classic "whodunit" is less about "crime" than about puzzle. Perhaps that is why we disagree. I never tell people I read "crime" -- I read mysteries!