The inspector general’s office of the Health and Human Services Department concluded yesterday that Bush Administration officials did not violate the law when they withheld information about the high costs of the planned Medicare overhaul last year. Congress passed the administration’s Medicare bill based on an estimated cost of about $400 billion. In January, Bush announced the overhaul would actually cost $534 billion over 10 years. Democratic lawmakers initiated an investigation when the HHS chief actuary Richard Foster announced in March that top administrator Tom Scully had threatened to fire him if he released that information to legislators during the Congressional debate. Bush’s plan overhauled the healthcare program for 41 million senior and disabled beneficiaries by increasing the role of private insurance companies, health maintenance organizations and drug-benefit managers.