Parkinson's disease (PD) is a degenerative movement disorder causing progressive disability that severely affects patients' quality of life. While early treatment can produce significant benefits for patients, the mildness of many early signs combined with the lack of accessible high-frequency monitoring tools may delay clinical diagnosis. To meet this need, user interaction data from consumer technologies have recently been exploited towards unsupervised screening for PD symptoms in daily life. Similarly, this work proposes a method for detecting fine motor skills decline in early PD patients via analysis of patterns emerging from finger interaction with touchscreen smartphones during natural typing. Our approach relies on low-/higher-order statistical features of keystrokes timing and pressure variables, computed from short typing sessions. Features are fed into a two-stage multi-model classification pipeline that reaches a decision on the subject's status (PD patient/control) by gradually fusing prediction probabilities obtained for individual typing sessions and keystroke variables. This method achieved an AUC = 0.92 and 0.82/0.81 sensitivity/specificity (matched groups of 18 early PD patients/15 controls) with discriminant features plausibly correlating with clinical scores of relevant PD motor symptoms. These findings suggest an improvement over similar approaches, thereby constituting a further step towards unobtrusive early PD detection from routine activities.