In this paper we explore the distortion performance of distributed estimation schemes in wireless sensor networks (WSNs) in the presence of an eavesdropper. The sensors use an uncoded amplify and forward scheme to transmit their observations to the fusion center (FC), which at the same time can be overheard by the eavesdropper. Both the FC and the eavesdropper reconstruct a minimum mean squared error (MMSE) estimate of the physical quantity observed. In this paper, we address the problem of transmit power allocation for system performance optimization subject to a total average power constraint on the sensors and a security constraint on the eavesdropper. In the case of full channel state information (CSI) the proposed scheme allows the sensors to adapt their transmission strategy based on the instantaneous channel gains of both the FC and the eavesdropper. In the partial CSI case, transmit power is allocated only according to the FC instantaneous channel gains and statistical channel gains of the eavesdropper. Numerical results illustrate the performance of the power allocation algorithms.