The couple flagged down officers in the area for help, Sgt. Lee Jones, a department spokeswoman, told The Washington Post on Sunday. But they could not retrieve the ring. The couple left without filing a police report or providing their contact information.
Officers returned to the scene on Saturday morning, removed the grate and recovered the ring, then launched a social media campaign to find the couple.
Nearly 12,000 people have retweeted the video since Saturday, drawing numerous puns from the public. One choice response, channeling Beyoncé: "He should have put a string on it."
The department cleaned the ring and posted photos of it taped to a chair on social media, along with surveillance photos of the couple. But there have not been any promising leads, Jones said.
The woman is just over 5 feet tall and has blond hair, the department said. The man is about 5-foot-10 with a "manicured beard."
The story has grabbed headlines, with one calling it a "romantic" proposal.
It's also 2018, when prosecutors alleged that the tale of a generous homeless man giving his last few dollars to a stranded couple - captivating the nation and cajoling it into giving him $400,000 - was an elaborate hoax.
There was room for doubt early on. The moment would be groan-worthy in a made-for-TV rom-com.
And maybe just as predictably, their story has a happy ending.
On Sunday afternoon, New York police said the unfortunate pair, who are from England, had heard the authorities "were looking for them."
"We're making arrangements to get them their ring back. Congratulations!" the police tweeted.