The opinion (.pdf) was written by retiring Justice Sandra Day O'Connor, a key swing voter at the court on abortion rights.
Justices said a lower court went too far by permanently blocking the law that requires a parent to be told before a daughter ends her pregnancy.
An appeals court must now reconsider the law, which requires that a parent be informed 48 hours before a minor child has an abortion but makes no exception for a medical emergency that threatens the youth's health.
In what may be O'Connor's last ruling of her career, she said "in this case, the courts below chose the most blunt remedy."
But the remedy wasn't necessarily a surprise, reports CBS News legal analyst Andrew Cohen.
"This scenario — sending the case back down for more consideration — was discussed at length during the oral argument on the case so I'm not sure that the parties here are terribly surprised that the Court would punt on the merits and perhaps avoid the issue altogether," Cohen said. "The Court frequently does this, in cases large and small."
The court had been asked to consider whether the 2003 law put an "undue burden" on a woman in choosing to end a pregnancy. O'Connor is an architect of the undue burden standard, and was the deciding vote in the last abortion case five years ago, when the justices ruled that a Nebraska law banning a type of late-term abortion was too burdensome. That law did not have an exception to protect the mother's health.
Instead, justices did not deal directly with that question.
The opinion, just a brief 10 pages, was a victory for New Hampshire and had been closely watched by other states with restrictions. Justices had been told that 24 states mandate a parent's approval and 19, including New Hampshire, demand parental notice.
"In the case that is before us ... the lower courts need not have invalidated the law wholesale," O'Connor wrote.
That means, Cohen said: "The Court is telling New Hampshire, and the lower court, that those provisions of that statute that are not legally suspect ought to be allowed to go into effect. That there is no reason now to block the whole notification effort just because there is a great controversy over one part of it."
"Only a few applications of New Hampshire's parental notification statute would prevent a constitutional problem. So long as they are faithful to legislative intent, then, in this case, the lower courts can issue a declaratory judgment and an injunction prohibiting the statute's unconstitutional application," the opinion read.