Is hand-writing analysis used for analysis of a person's behaviour or anlayzing a person's character? Does the handwriting analysis of a person predict only his/her behavior or only his/her character or both?
The professional term for hand-writing analysis seems to be "Graphology" and there is no clear evidence that it could be used to predict a person's behaviour or character. For a starting point see the wikipedia page, then there are this article in the New York Times from 1993 and this more recent article from BBC from 2005 for more casual explanations of the phenomenon.

For more scientific references there is this paper from 1983 and this one from 1987 that both fail to show significant results. Also this book chapter might give a good overview but I can only tell from the abstract and you would have to find it at a library or purchase it somehow.

References


Rafaeli, A., &amp; Klimoski, R. J. (1983). Predicting sales success through handwriting analysis: An evaluation of the effects of training and handwriting sample content. Journal of Applied Psychology, 68(2), 212.
Beyerstein, B. L. (2007). Graphology—a total write-off. Tall Tales about the Mind &amp; Brain: Separating Fact from Fiction, 233-70.
Furnham, A., &amp; Gunter, B. (1987). Graphology and personality: Another failure to validate graphological analysis. Personality and Individual Differences, 8(3), 433-435.