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NPR reports that SCOTUS declined to hear the long-standing case, in which Michael Skidmore, an heir for Spirit frontman Randy Wolfe, alleged similarities between the instrumental intro of "Stairway to Heaven" and Spirit's "Taurus."
The legal battle began in 2014, and a jury ruled in favor of Led Zeppelin in 2016, the outlet reports.
In March, the 9th Circuit Court of Appeals upheld a ruling that the song was not copied.
Francis Malofiy, the attorney for Wolfe's estate, told Fox Business that the band won "on a technicality," as the jury allegedly was not allowed to listen to the song, but rather examined written score submitted to the U.S. Copyright Office.
"This lawsuit was about giving credit where credit was due: We accomplished that goal," the attorney said.
In 2014, Spirit bassist Mark Andes said that Wolfe, known as Randy California, never filed his own suit against Led Zeppelin -- specifically Jimmy Page and Robert Plant -- due to lack of resources, People magazine reports.
Wolfe drowned in 1997 while saving his 12-year-old son Quinn, who had been caught in a rip current in Hawaii. Quinn survived the ordeal.
Reps for Led Zeppelin did not immediately respond to FOX Business' request for comment.