WASHINGTON — The Bush administration violated federal law last year when it restricted states’ ability to provide health insurance to children of middle-income families, and its new policy is therefore unenforceable, lawyers from the Government Accountability Office said Friday. The ruling strengthens the hand of at least 22 states, including New York and New Jersey, that already provide such coverage or want to do so. And it significantly reduces the chance that the new policy can be put into effect before President Bush leaves office in nine months. At issue is the future of the State Children’s Health Insurance Program, financed jointly by the federal government and the states. Congress last year twice passed bills to expand the popular program, and Mr. Bush vetoed both. State officials of both parties say the policy, set forth in a letter to state health officials on Aug. 17, has stymied their efforts to cover more children at a time when the number of uninsured is rising and more families are experiencing economic hardship. In a formal legal opinion Friday, the accountability office said the new policy ‘amounts to a marked departure’ from a longstanding, settled interpretation of federal law. […]