In this paper, we investigate the distortion outage minimization problem for a wireless sensor network (WSN) in the presence of an eavesdropper. The observation signals transmitted from the sensors to the fusion center (FC) are over-heard by the eavesdropper. Both the FC and the eavesdropper reconstruct minimum mean squared error (MMSE) estimates of the physical quantity observed. We address the problem of transmit power allocation to minimize the distortion outage at the FC, subject to a long-term transmit power constraint among the sensors and a secrecy outage constraint at the eavesdropper. Applying a rigorous probabilistic power allocation technique we derive power policies for the full channel state information (CSI) case. Additional suboptimal power control policies are studied for the partial CSI case in order to reduce the high computational cost as the number of sensors or receive antennas grows. Numerical results show better performance can be achieved by adding multiple receive antennas at the FC.