Critical thinking plays a part in every aspect of a criminal investigation. In fact, it is hard to think that any investigation could succeed without critical thinking.
For example, when a crime has been committed, it is always important to ask who might have had a motive to commit the crime. This requires critical thinking about the nature of the crime and the possible ways in which someone might benefit from it. As another example, it might be important to try to determine if the crime is linked to other crimes that have been committed. Critical thinking is needed in such a case because investigators must ask themselves which aspects of the crime might be unique enough to serve as "fingerprints" of a given criminal.
Since a criminal investigation is all about using clues to determine what has happened, critical thinking is a must.