While you should consult with an attorney who has experience in lawsuits against the police, there is a good chance that you do not have effective recourse: the police are, appropriately, given a great deal of discretion in discharging their duties, since they couldn't do their jobs if they were constantly being second-guessed and sued. As a  result, police misconduct must be more than merely negligent to typically result in liability--i.e. it needs to be more than a mistake or poor judgment. It usually requires either a deliberate wrongdoing or recklessness--a gross disregard for the risks or the facts of the situation. In a case like this, responding to a child's 911 call (even if it was an error) and so understandably "keyed up," and confronted by a dog which was barking and getting closer, it is doubtful that the police officer, as bad as his judgment clearly was, acted sufficiently wrongful so as to support recovery.In addition, given that even if there were liabiltiy, the most you could likely recover would be the dog's medical costs--it is rare that you can recover for emotional upset, like your daughter is experiencing--which could be offset by the cost of litigation.