No other information about the arrest has been released, and the staff at Simon's music company declined NBC New York's request for comment.
"We're going to go home and watch our son play baseball," Simon told the judge. "We had an argument, which is atypical of us. Neither of us has any fear, or any reason to be threatened."
Brickell added, "He's no threat to me at all."
UPDATE 12:11 pm: From the Associated Press:
A caller from the singers' New Canaan home dialed 911 Saturday night and hung up, police chief Leon Krolikowski said at a news conference Monday. Officers who responded found minor injuries and believed it was a case of domestic violence, he said. He did not say who was injured.
Simon and Brickell, who have been married for more than two decades, were each given a misdemeanor summons and one of them agreed to leave and go to another location, Krolikowski said.
"There was aggressiveness on both sides," he said. "They're both victims and they have children involved and we're trying to be very cautious of that."
An arraignment is scheduled for Monday afternoon.
[Image via AP]