This paper presents an automatic algorithm for the detection of respiratory events in patients using electrocardiogram (ECG) and respiratory signals. The proposed method was developed using data of polysomnogram (PSG) and those recorded from a patch-type device. In total, data of 1,285 subjects were used for algorithm development and evaluation. The proposed method involved respiratory event detection and apnea-hypopnea index (AHI) estimation. Handcrafted features from the ECG and respiratory signals were applied to machine learning algorithms including linear discriminant analysis, quadratic discriminant analysis, random forest, multi-layer perceptron, and the support vector machine (SVM). High performance was demonstrated when using SVM, where the overall accuracy achieved was 83% and the Cohen's kappa was 0.53 for the minute-by-minute respiratory event detection. The correlation coefficient between the reference AHI obtained using the PSG and estimated AHI as per the proposed method was 0.87. Furthermore, patient classification based on an AHI cutoff of 15 showed an accuracy of 87% and a Cohen's kappa of 0.72. The proposed method increases performance result, as it records the ECG and respiratory signals simultaneously. Overall, it can be used to lower the development cost of commercial software owing to the use of open datasets.