Crooked city runs investigation (8)
I believe the answer is:
scrutiny
'investigation' is the definition.
(scrutiny is a kind of investigation)
'crooked city runs' is the wordplay.
'crooked' is an anagram indicator.
'city'+'runs'='cityruns'
'cityruns' with letters rearranged gives 'SCRUTINY'.
(Other definitions for scrutiny that I've seen before include "Intense study" , "Critical examination" , "Close investigation" , "A careful look or examination" , "Close, careful examination" .)