Obstructive sleep apnea (OSA) is believed to contribute significantly to atrial fibrillation (AF) development in certain patients. Recent studies indicate a rising risk of AF with increasing OSA severity. However, the commonly used apnea-hypopnea index in clinical practice may not adequately account for the potential cardiovascular risks associated with OSA. 1) Objective: to propose and explore a novel method for assessing OSA severity considering potential connection to cardiac arrhythmias. 2) Method: the approach utilizes cross-recurrence features to characterize OSA and AF by considering the relationships among oxygen desaturation, pulse arrival time, and heart-beat intervals. Multinomial logistic regression models were trained to predict four levels of OSA severity and four groups related to heart rhythm issues. The rank biserial correlation coefficient, rrb, was used to estimate effect size for statistical analysis. The investigation was conducted using the MESA database, which includes polysomnography data from 2055 subjects. 3) Results: a derived cross-recurrence-based index showed a significant association with a higher OSA severity (p 0.01) and the presence of AF (p 0.01). Additionally, the proposed index had a significantly larger effect, rrb, than the conventional apnea-hypopnea index in differentiating increasingly severe heart rhythm issue groups: 0.14 0.06, 0.33 0.10, and 0.41 0.07. 4) Significance: the proposed method holds relevance as a supplementary diagnostic tool for assessing the authentic state of sleep apnea in clinical practice.