The police actually have 0 liability if they don't show up(Warren v. District of Columbia).
Basically two women were up in their apartment, and heard their friend screaming at the bottom of a stair well. They then called the police, and after awhile the screaming stopped, and they assumed the police had arrived, and went out to check. What they found was their friend beat up, and the intruder, who then ordered them up to the room and held them hostage and beat, raped, robbed, and forced them to preform sexual acts on each other and himself for the next 14 hours.
