With about 16 percent of its residents uninsured, Washington state falls solidly in middie of the pack, with Texas having the highest percentage of residents without health insurance: more than 25 percent. Massachusetts, where a state health-insurance mandate has been in place for years, has the smallest percentage of uninsured residents at just under 5 percent. But in one way, and not a good one, Washington nearly led the nation, a recent report revealed. From 2008 to 2011, the state's increase in the number of residents without insurance was second-highest.