Parametric analysis of Cerebellar Ataxia (CA) could be of immense value compared to its subjective clinical assessments. This study focuses on a comprehensive scheme for objective assessment of CA through the instrumented versions of 9 commonly used neurological tests in 5 domains- speech, upper limb, lower limb, gait and balance. Twenty-three individuals diagnosed with CA to varying degrees and eleven age-matched healthy controls were recruited. Wearable inertial sensors and Kinect camera were utilised for data acquisition. Binary and multilabel discrimination power and intra-domain relationships of the features extracted from the sensor measures and the clinical scores were compared using Graph Theory, Centrality Measures, Random Forest binary and multilabel classification approaches. An optimal subset of 13 most important Principal Component (PC) features were selected for CA-control classification. This classification model resulted in an impressive performance accuracy of 97% (F1 score = 95.2%) with Holmesian dimensions distributed as 47.7% Stability, 6.3% Timing, 38.75% Accuracy and 7.24% Rhythmicity. Another optimal subset of 11 PC features demonstrated an F1 score of 84.2% in mapping the total 27 PC across 5 domains during CA multilabel discrimination. In both cases, the balance (Romberg) test contributed the most (31.1% and 42% respectively), followed by the peripheral tests whereas gait (Walking) test contributed the least. These findings paved the way for a better understanding of the feasibility of an instrumented system to assist informed clinical decision-making.