Titled "Like to Get to Know You," the song is a gentle acoustic ballad about finding new faith in old love. "I wouldn't trade places with anyone," the pair, married since 1992, harmonize. "Because I'd like to get to know you again."
"I know how you like your coffee," Simon sings. Brickell's rejoinder: "And I know how bad you drive."
Comments on the song are disabled on Brickell's Soundcloud page.
The couple were arrested April 26 at their New Canaan, Conn. home. According to police, Simon called police after he and Brickell got in a physical scuffle that left both with minor injuries.
"I got my feelings hurt and picked a fight with my husband. The police called it disorderly. Thank God it's orderly now," Brickell told PEOPLE in a statement through her lawyer.
In court in Norwalk, Conn., on Monday, the pair played down the incident.
"Both of us are fine together," Simon told the court. Brickell agreed: "He is not a threat to me at all."
The couple are due to return to court on May 16.