A new study just published in the Archives of Internal Medicine showed that increasing severity of sleep apnea is associated with a progressively increasing risk of atrial fibrillation and ventricular arrhythmias.
The type of sleep apnea matters:
It's possible that treating sleep apnea could improve the arrhythmia, but there's currently no proof of that. The study was done on men, but likely applies to women, too.
To learn more, read: Sleep Apnea Severity Increases the Risk of Atrial Fibrillation and Ventricular Arrhythmias