The mayor says many of the complaints are unfounded.
Weis was ordered to provide the list to lawyers for Donna Moore, who is suing the city. She claims an officer physically attacked her 11-year-old son and 13-year-old daughter during a dispute with his son in 2007.
"My children were harmed by people who were supposed to protect us," Moore said.
One of the lawyers representing Moore, Flint Taylor, is calling for Weis to resign or be fired.
In court papers, Weis said turning over the names of the officers would compromise officers' performance, threaten safety and lower morale.
Weis has also refused to turn over a similar list of officers with excessive force complaints.
