This paper presents the development and evaluation of a method for enabling quantitative and automatic scoring of alternating tapping performance of patients with Parkinson’s disease (PD). Ten healthy elderly subjects and 95 patients in different clinical stages of PD have utilized a touch-pad handheld computer to perform alternate tapping tests in their home environments. First, a neurologist used a web-based system to visually assess impairments in four tapping dimensions (‘speed’, ‘accuracy’, ‘fatigue’ and ‘arrhythmia’) and a global tapping severity (GTS). Second, tapping signals were processed with time series analysis and statistical methods to derive 24 quantitative parameters. Third, principal component analysis was used to reduce the dimensions of these parameters and to obtain scores for the four dimensions. Finally, a logistic regression classifier was trained using a 10-fold stratified cross-validation to map the reduced parameters to the corresponding visually assessed GTS scores. Results showed that the computed scores correlated well to visually assessed scores and were significantly different across Unified Parkinson’s Disease Rating Scale scores of upper limb motor performance. In addition, they had good internal consistency, had good ability to discriminate between healthy elderly and patients in different disease stages, had good sensitivity to treatment interventions and could reflect the natural disease progression over time. In conclusion, the automatic method can be useful to objectively assess the tapping performance of PD patients and can be included in telemedicine tools for remote monitoring of tapping.