Accurate network topology information is critical for secure operation of smart power distribution systems. Line outages can change the operational topology of a distribution network. As a result, topology identification by detecting outages is an important task to avoid mismatch between the {topology that the operator believes is present and the actual topology}. Power distribution systems are operated as radial trees and are recently adopting the integration of sensors to monitor the network in real time. In this paper, an optimal sensor placement solution is proposed that enables outage detection through statistical tests based on sensor measurements. Using two types of sensors, node sensors and line sensors, we propose a novel formulation for the optimal sensor placement as a cost optimization problem with binary decision variables, i.e., {to place or not place a sensor at each bus/line}. The advantage of the proposed placement strategy for outage detection is that it incorporates various types of sensors, is independent of load forecast statistics and is cost effective. Numerical results illustrating the placement solution are presented.