The decision affirms a lower court ruling and means Happy will not be released to a more spacious sanctuary through a habeas corpus proceeding, which is a way for people to challenge illegal confinement.
Extending that right to Happy to challenge her confinement at a zoo "would have an enormous destabilising impact on modern society". And granting legal personhood in a case like this would affect how humans interact with animals, according to the majority decision.
"Indeed, followed to its logical conclusion, such a determination would call into question the very premises underlying pet ownership, the use of service animals and the enlistment of animals in other forms of work," read the decision.
Operators of the Bronx Zoo argued Happy is neither illegally imprisoned nor a person, but a well-cared-for elephant "respected as the magnificent creature she is".
The advocates at the Nonhuman Rights Project argued that Happy is an autonomous, cognitively complex elephant worthy of the right reserved in law for "a person".
Judges Rowan Wilson and Jenny Rivera wrote separate, sharply worded dissents saying the fact that Happy is an animal does not prevent her from having legal rights. Rivera wrote that Happy is being held in "an environment that is unnatural to her and that does not allow her to live her life".
"Her captivity is inherently unjust and inhumane. It is an affront to a civilised society, and every day she remains a captive — a spectacle for humans — we, too, are diminished," Rivera wrote.
The ruling from New York's highest court cannot be appealed. The Nonhuman Rights Project has failed in similar cases, including those involving a chimpanzee named Tommy in upstate New York.
Steven Wise, the group's founder, said he was pleased it managed to persuade some of the judges. He noted that the group has a similar case under way in California and more planned in other states and other countries.
"We will take a close look at why we lost and we'll try to make sure that that doesn't happen again to the extent that we can," he said.
Happy was born in the wild in Asia in the early 1970s, captured and brought as a 1-year-old to the United States. She arrived at the Bronx Zoo in 1977 with fellow elephant Grumpy, who was fatally injured in a 2002 confrontation with two other elephants.