After the incident, Happy was briefly paired with another elephant, which also died.
Happy has been kept apart from the elephants that injured her mate, the New York Daily News reports. The publication cites advocates who say Happy is highly intelligent and demonstrated signs of self-recognition in 2005.
In a Tuesday release, the Nonhuman Rights Project cites a New York Court of Appeals concurring opinion that stopped short of calling a chimpanzee a person, but said "there is no doubt that it is not merely a thing," according to the group.
The group's petition was filed nearly 300 miles away from the zoo's location, as judges closer to the zoo have not embraced the idea that animals have legal rights like people.
The zoo has criticized the petition: "The Nonhuman Rights Project is exploiting the Bronx Zoo elephants to advance their own failing cause in the courts as they put forth ludicrous legal arguments and lies about our elephants, facilities and staff," said Bronx Zoo Director Jim Breheny.
Happy is content and well-cared for, the zoo says. Moving her would not be in her best interest, according to Breheny.
"Happy is healthy and comfortable in the home she has known for nearly four decades. Our animal care professionals say she exhibits no signs of physiological or psychological stress with virtually no stereotypical behavior," Breheny wrote.
Associated Press reports were used in this article.