Here is a free full text review on the associations.
From the review:
Parathyroid hormone (PTH) acts on G-protein coupled receptors in the heart to exert changes in cardiac myocyte contractility, proliferation, and hypertrophy.
In the vasculature, PTH alters the endothelium.
Excess PTH (as seen in primary and secondary hyperparathyroidism) is associated with a higher incidence of hypertension, left ventricular hypertrophy, heart failure, cardiac arrhythmias, and valvular calcific disease, which may contribute to higher cardiac morbidity and mortality.
Low PTH states (as seen in congenital and acquired disorders of the parathyroid glands) are associated with cardiac arrhythmias and dilated cardiomyopathy.
Early medical and/or surgical treatment of parathyroid disorders can reverse detrimental structural and functional changes in the cardiovascular system such as left ventricular mass, conduction abnormalities, atherosclerotic disease, and valvular calcifications. This may result in reduced cardiac morbidity and mortality.