Monitoring the heart rhythm during out-of-hospital cardiac arrest (OHCA) is important to improve treatment quality. OHCA rhythms fall into five categories: asystole (AS), pulseless electrical activity (PEA), pulse-generating rhythms (PR), ventricular fibrillation (VF) and ventricular tachycardia (VT). This paper introduces an algorithm to classify these OHCA rhythms using the ECG and the thorax impedance (TI) signals recorded by the defibrillation pads. The dataset consisted of 100 OHCA patient files from which 2833 4-s signal segments were extracted: 423 AS, 912 PE, 689 PR, 643 VF, and 166 VT The Stationary Wavelet Transform (SWT) was used to obtain 95 features from the ECG and the TI. Random Forest classifiers were used, features were ranked during training using random forest importance, and models with increasing number of features were evaluated. The optimal classifier was obtained combining 50 ECG and TI features, with a median (80% confidence interval) average recall of 86.5% (80.6-89.4). The recall for AS/PEA/PR/VF/VT were 96.3% (93.0-98.5), 77.8% (68.1-89.2), 88.7% (79.5-93.6), 94.4% (90.2-97.4) and 77.3% (52.9-91.3), respectively.