We discuss some aspects of the extension to continuous systems of a statistical measure of complexity introduced by López-Ruiz, Mancini, and Calbet [Phys. Lett. A 209, 321 (1995)]. In general, the extension of a magnitude from the discrete to the continuous case is not a trivial process and requires some kind of choice. In the present study, several possibilities appear available. One of them is examined in detail. Some interesting properties desirable for any magnitude of complexity are discovered on this particular extension.