This study investigates signals from sustained phonation and text-dependent speech modalities for Parkinson's disease screening. Phonation corresponds to the vowel /a/ voicing task and speech to the pronunciation of a short sentence in Lithuanian language. Signals were recorded through two channels simultaneously, namely, acoustic cardioid (AC) and smart phone (SP) microphones. Additional modalities were obtained by splitting speech recording into voiced and unvoiced parts. Information in each modality is summarized by 18 well-known audio feature sets. Random forest (RF) is used as a machine learning algorithm, both for individual feature sets and for decision-level fusion. Detection performance is measured by the out-of-bag equal error rate (EER) and the cost of log-likelihood-ratio. Essentia audio feature set was the best using the AC speech modality and YAAFE audio feature set was the best using the SP unvoiced modality, achieving EER of 20.30% and 25.57%, respectively. Fusion of all feature sets and modalities resulted in EER of 19.27% for the AC and 23.00% for the SP channel. Non-linear projection of a RF-based proximity matrix into the 2D space enriched medical decision support by visualization.