Brickell told officers she confronted her husband after he did something to "break her heart," according to police, but she did not provide any details. She told police he shoved her during the argument, and she slapped him.
The report indicates Simon called 911 and then hung up, prompting the police response.
Simon suffered a superficial cut to his ear, and Brickell, who smelled of alcohol, had a bruise on her wrist, according to the police report, first obtained by the Hour of Norwalk on Tuesday.
Message seeking comment were left Thursday with attorney Allan Cramer, who is representing the couple in the case.
Brickell told police the two had other physical confrontations and asked an officer to feel a lump on her head. But she would not let police photograph her injuries and declined to elaborate on the other confrontations.
The couple were allowed to remain on the property, but Simon agreed to spend the night in a second home in Manhattan, police said.
Both said in court Monday they did not consider the other a threat, and no protective order was issued. They are due back in court on May 16.
"Both of us are fine together," Simon told Superior Court Judge William Wenzel. "We had an argument and it's atypical of us and neither one of us has any fear or any reason to feel threatened."
"He's no threat to me at all," Brickell added.
A duet by the pair "Like To Get To Know You" was posted on Brickell's website on Wednesday.
The lyrics are about a couple having problems but ends with the hopeful line, "I'd like to get to know you, again."
Simon and Brickell were married in 1992. They have three children together.
Simon burst onto the national stage with his former partner Art Garfunkel in the 1960s, adding a gentle voice to the growing chorus of opposition to the Vietnam War. Brickell, meanwhile, gained fame for her songs that blend rock, folk, blues and jazz.