In the 1961 case of Monroe v. Pape, the Monroe family filed suit against the Chicago PD and several individual officers for an illegal search of their home and an unlawful detention of Mr. Monroe. And they won. But the city of Chicago appealed all the way to the Supreme Court arguing that the Monroes could only sue the officers and not the city. The Supreme Court ruled in favor of the city.
Still, Monroe was a very important case. It marked the first time that a major police department had been sued for a federal civil rights violation and the plaintiffs prevailed. Some 20 odd years later, the Supreme Court changed its mind in the Monell case. The details of Monell don't really involve law enforcement. However, the decision in Monell made government entities vulnerable to civil rights lawsuits that stem from the actions of their employees.