Handwriting is a mode of communication. It is just like speaking. You must have seen a person speaking something but his body language his gestures, eyes and tone of voice is telling you something else. So there are two aspects of this communication, verbal and non-verbal communication.
Similarly, when you write, there are two things happening. One, you are conscious about the content, the phrasing of sentence, spelling of words etc while you are composing your written communication. Two, you are unaware of the subconscious activity of handwriting formations. You are not conscious about whats happening with the f's t's a's and y's in your writing.
The handwriting formations are occurring to you subconsciously.
About Crime: When a person is narrating a crime incidence in which he is involved but he is lying, then you may see the contradiction between his verbal and non-verbal communication. Similarly, when a person is asked to write about a crime incidence he has witnessed, if there are discrepancies in the content and the formations then the person may be involved in the crime.
For example, there can be hesitation, change in writing slant, size pressure etc whenever a person is lying while writing. There is a conflict between the conscious mind and the subconscious mind. When the person knows that what he is writing is not true it will show up in his writing.
More the conflict in his mind more will be the prominence of such discrepancies.
Handwriting analysis is used to find white collar criminals. It requires skills to distinguish a person who has criminal tendencies and the one who is involved in the crime. A person who may have criminal tendencies who is a suspect may not be involved in the crime under investigation. A good handwriting analyst can make out the difference.
If you are a Graphologist:
The important term for crime investigation using graphology is "specific variation".
An advance application of Graphology in crime investigation is analysing the handwriting of the victim to understand who can cheat him and how. Understanding the psychology and way of thinking of the victim can also help you to understand the modus operandi of the criminal.