Handwritten script classification is still considered as a challenging research problem in the domain of document image analysis. Although some research attempts have been made by the researchers for solving the challenging issues, a comprehensive solution is yet to be achieved. The case study, undertaken here, analyzes the performances of various state-of-the art handwritten script classification methods for Indian scripts where features, needed for the script classification task, are extracted from the script images at four different granularity levels, i.e., page, block, text line, or word. The results of handwritten script classification at each level have been obtained and compared using eight different feature sets and six different state-of-the-art classifiers. Based on the classification results, an ideal level for performing the handwritten script classification task is suggested among these four classification levels. The results have also been improved by using two feature dimensionality reduction methods. All these experiments are done on two different handwritten Indic script databases, of which one is an in-house developed dataset and the other one is a freely available dataset. Finally, some future research directions that may be undertaken by the researchers as an application of the handwritten Indic script classification problem are also highlighted. The work presented here provides a basic foundation for the construction of a comprehensive handwritten script classification method for official Indian scripts.