CHICAGO—Police here stopped physically responding to some 911 calls for non-life-threatening issues this week so officers can focus on stemming the city's rising homicide rate, a strategy that other big cities have implemented with sometimes controversial results.

Under the new policy, dispatchers will route 911 calls reporting non-criminal complaints or crimes in which no one is in imminent danger, such as some car thefts and simple assaults, to desk officers who will fill out police reports by phone. The new policy prohibits...