But the nine justices did not release their decisions on several controversial cases, like the detention of "enemy combatants," the Guantanamo Bay prison and documents from Vice President Dick Cheney's energy task force.
Rulings in those cases are expected next Monday, the last of the court's current term.
The 5-4 decision on police identification frees the government to arrest and punish people who won't cooperate by revealing their identity.
The decision, reached by a divided court, was a defeat for privacy rights advocates who argued that the government could use this power to force people who have done nothing wrong to submit to fingerprinting or divulge more personal information.
Police, meanwhile, had argued that identification requests are a routine part of detective work, including efforts to get information about terrorists.
The justices upheld a Nevada cattle rancher's misdemeanor conviction. He was arrested after he told a deputy that he didn't have to reveal his name or show an ID during an encounter on a rural road in 2000.
"This is just the latest in a string of rulings from the Court that give law enforcement officials more power and authority over people even when there is no serious criminal activity afoot," said CBS News legal analyst Andrew Cohen. "And we ought to expect more of these rulings given the war on terrorism and the government's interest in trying to prevent crime and not just punish it."
In the malpractice case, the court said that patients who claim their HMOs wouldn't pay for needed medical care cannot sue for big malpractice damages, an issue at the heart of the long debate over efficiency versus service in managed health care.
The court was unanimous in saying that two HMO patients in Texas cannot pursue big malpractice or negligence cases against their insurers in state court, as they claimed a Texas patient protection law allowed them to do. Instead, they must go to federal court, where evidence standards are generally higher and damages awarded are usually lower than in state courts.
The managed care industry said the ruling would actually be good for patients because it would reduce lawsuits and make insurance more affordable, reports CBS News Correspondent Wyatt Andrews.
But the patients who brought the lawsuit called the ruling an injustice. Ruby Calad of Houston, was one of two Texas patients who claimed under state law their HMO's injured them by denying them care. Now says the state Attorney General, the HMOs are more free to do harm.
"What this does is it meaningfully limits the rights of patients to go to the courts, and get a court ruling or a jury ruling that HMOs have done wrong," said Attorney General Greg Abbott.
"This tosses the ball back into Congress' lap because Congress can easily solve this problem by changing the law to give patients more rights in federal court or to allow states to do what Texas did here, which is to give patients certain benefits under state law," Cohen said.
Four years ago Texas Governor and candidate George Bush said he was all for giving patients the right to sue.
When it got the Supreme Court however the Bush Administration argued the HMOs should be immune.
In rulings Monday the court also:
This is the second summer in a row in which the Supreme Court has ended its spring session in high drama. Last year, the court made last-minute, landmark rulings in cases involving and .
Last week, the nine justices dispatched one of the more controversial issues on its docket, the lawsuit of an atheist father opposed to the recitation of the .
In one of the remaining cases, the judges hold in their hands the futures of so-called Yaser Hamdi, captured on the battlefield in Afghanistan, and Jose Padilla, arrested in Chicago on suspicion of plotting a terrorist act.
Both are U.S. citizens. In both cases, the court is being asked whether constitutional protections against being locked up without trial apply in the war on terrorism.
In the case, lawyers for the prisoners have asked: Can foreign-born prisoners picked up overseas and held outside U.S. borders use American courts to try win their freedom? The Bush administration asserts that in war, the constitution gives the president broad powers.