The problem of energy-efficient resource allocation in multiple-antenna wiretap channels where transmit antennas are correlated is investigated. The use of artificial noise (AN) in combination with only statistical channel state information (CSI) at the legitimate transmitter is considered. The goal of this work is to do the resource allocation such that the amount of bits which can be reliably and confidentially transmitted per unit of consumed energy, namely, the secrecy energy efficiency (SEE), is maximized. The resulting non-convex maximization problems are tackled by means of fractional programming and sequential convex optimization tools, and first-order optimal solutions are obtained with polynomial complexity. Numerical results show the merits of the proposed algorithms.