Connecticut hospitals are asking the federal government to declare that the state is violating federal law by paying inadequate reimbursements for treating Medicaid patients while imposing a $556 million tax on the industry that health care providers say has jeopardized care.

In a petition filed Tuesday with the Centers for Medicare and Medicaid Services, the Connecticut Hospital Association and 21 hospitals accused the state of running an “illegal reimbursement scheme” in violation of federal law, and asked the agency to bring the state’s rates and payments in line with requirements under the Medicaid Act.