Oops, I mis-spoke. The legal duty was established the moment the city agreed to send a patrol car to the location. “. . . [V]oluntary assumption of a duty to act carrie[s] with it the obligation to act with reasonable care.” Furthermore, it can likely be established that the victim
relied to her detriment that the police would promptly respond. In other words, her attorney will likely argue that, for example, the victim did not flee the area because she believed the police were on the way.
The seminal case (where the above quote and reasoning appear) in this regard is a 1982 case, DeLong v. Erie County., 89 A.D.2d 376, 455 N.Y.S.2d 887. It is taught to most first-year law students.
The city will settle out of court.
It goes to whether they acted with reasonable care, not to the concept of police protection, though. If the cops had acted with reasonable care and it still took them 17 minutes to get there, there'd be no cause of action, yes?