Ill-natured American police department (4)
I believe the answer is:
acid
'ill-natured' is the definition.
'american police department' is the wordplay.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'police department' becomes 'cid' (I've seen this in other clues).
'a'+'cid'='ACID'
(Other definitions for acid that I've seen before include "So-called drug" , "Alkali's opposite" , "Drug LSD (colloq.)" , "Bitter or sour" , "Vinegary" .)