After watching a harmless fee turn into a hefty, increasing tax in just three years, Connecticut's hospitals say a phase-out of the state provider tax is essential to preserve health care services and jobs. With Gov. Dannel P. Malloy's new biennial budget plan due in just eight days, the Connecticut Hospital Association proposed this week phasing out the provider tax over the next five years. "The hospital tax costs Connecticut hospitals $254 million every year," CHA spokeswoman Michele Sharp said Monday. "It means they must provide care with even fewer resources" and make fewer investments in staff, medical equipment and other infrastructure.