The state’s top insurers were more likely to approve claims for mental health services in 2015 than the year before, but rates of rejection for residential care remained high, a new state report shows. About 6.4 percent of claims for mental health services were rejected by eight top managed care insurers – down from about 8 percent in 2014 – according to an analysis of the 2016 Consumer Report Card on Health Insurance Carriers in Connecticut. At the same time, insurers continued to deny more than one in six requests for residential behavioral health care. And the percentage of managed care plan enrollees who received any inpatient services for mental health was low, with most companies providing such services for fewer than 0.3 percent of all enrollees. The analysis is based on eight companies that reported the same categories of data in 2015 and 2016 to the state Insurance Department, which changed the reporting format across the two years.