Detective's joke sounds a bit crude (8)
I believe the answer is:
homespun
'crude' is the definition.
(thesaurus)
'detective's joke' is the wordplay.
'detective's' becomes 'homes' (I can't explain this - if you can you should give a lot more credence to this answer).
'joke' becomes 'pun' (pun is a type of joke).
'homes'+'pun'='HOMESPUN'
'sounds a bit' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
(Other definitions for homespun that I've seen before include "Folksy - open mush (anag)" , "Simple, unsophisticated" , "Artless and straightforward" , "Unsophisticated - not made in mill" , "Rustic" .)