Yes. One of symptoms of CAD is chest pain called Angina. Angina can spread to back, jaw, neck, and left shoulder, left arm. Only left shoulder & left arm, rarely right side. When the heart is lack of enough blood and oxygen, it starts to squeeze the heart and the muscle near the heart area to get more blood and oxygen. This is the cause of the pain. Usually, when people feel pain in left shoulder or left arm from time to time caused by ischemia, it usually gets severe in a few days. So if it's a chronic arm pain, it's less likely connected with heart.