Thousands of newly insured Massachusetts residents are still relying on emergency rooms for routine medical care. Under a 2006 law, nearly every state resident is required to have health insurance, and the law's framers hoped it would ease overuse of ERs as the newly insured went instead to primary care doctors for non-urgent health needs. But a sizable number of patients who obtained state-subsidized insurance have continued to use the ER at a rate 14% higher than Massachusetts residents overall, according to records.