Crook cites police constable as a doubter (7)
I believe the answer is:
sceptic
'doubter' is the definition.
(synonyms)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for sceptic that I've seen before include "One habitually doubts accepted beliefs" , "A doubting Thomas" , "One doesn't believe" , "Greek philosopher" , "I may doubt that" .)