Should we convert independent continous variables (features) to categorical variable before using decision tree like classifier? Consider I have one dependent variable to predict 'Attitude' which can take three values 'Positive/Negative/Neutral'.
I have following independent variables or features- Age, Height, Gender, Income etc. I trying to predict Attitude using decision tree classifier.

Attitude ~ Age + Height + Gender + Income (Decision Tree) 

I am getting >90% accuracy for the when tree depth is 15. As tree is dividing on continuous variables (i.e. Age, Income and Height) again and again to get leaf with pure classes. 

Is this problem of overfitting? Should I convert the continuous variables into categorical variables (like range classes)?
There is no need to split continuous variables because the tree already does that automatically. The only way you can test for overfitting is by either using a holdout set or by doing cross validation. If you are overfitting, changing a continuous variable to a categorical variable likely won't make a difference. If you get the sense that you're overfitting, you should reduce the depth of your tree.