Katy Perry’s new single, “Broken,” sounds familiar, it’s not your imagination. The same song, with minor lyrical revisions, was released as a single in 2003 by San Diego’s sister-fronted pop group the Troys under the title “What Do You Do.” The single was the only song released from the Troys’ shelved Elektra album Massaging Your Ego.

The two songs’ common thread is the hit production team of Lauren Christy, Graham Edwards, and Scott Spock, collectively known as the Matrix (Avril Lavigne, Korn). They are listed on performing-rights organization BMI’s website as songwriters, alongside sisters Anna and Lindsey Troy. All five receive credit on both versions of the song. Neither the Matrix nor their representatives could be reached for comment.

There are other similarities between the two tracks. Perry’s song also dates back to 2003, part of a similarly shelved, Matrix-produced album. The self-titled CD was finally released this January to cash in on Perry’s “I Kissed a Girl” success.

For her part, Anna Troy was surprised to see Perry on YouTube singing a song she cowrote. “The first I knew about it was when the video showed up on YouTube,” she said. Troy has had no contact with the Matrix producers since Elektra dropped her project in 2004. “Surreal is not a strong enough word for this. It’s strange to have something like this pop up out of nowhere; that whole era of my music seems like so long ago.”

The Troys’ contributions were primarily lyrical. “They played us the shell of the song on acoustic guitars, and then we jammed on ideas for the words,” she recalled. The sisters cowrote three more songs with the Matrix; however, all are unreleased. Though their planned album never materialized, “What Do You Do” was released as a single and received MTV airplay. It was also included on a soundtrack album for the Powerpuff Girls cartoon and is part of several karaoke collections. In 2003, “What Do You Do” was a Song of the Year nominee at the San Diego Music Awards. The following year, it was also one of the eight cited songs that earned the Matrix a 2004 Grammy nomination as Producers of the Year.

Though there will likely be some financial benefit to Perry’s cover, Troy laughs at the suggestion that it might be much. “It’s just a small percentage to begin with, and then it’s split five ways, with us getting the smaller share. Nobody is going to be retiring anytime soon.”

Bart Mendoza has collaborated with Anna Troy.