The question of whether the finite values of the correlation dimension (D2), used as an index of EEG complexity are due to its chaotic nature or they reflect its behaviour as linearly-correlated noise, remains open. This report aims at clarifying this by measuring D2 and analysing the non-linear nature of EEG through the method of surrogate data as well as by calculating the fractal exponent (beta) via coarse graining spectral analysis (CGSA) in nine adult subjects during waking and sleep states. The results show that even if it is possible to get an estimation of D2 in all states, non-linear structure appears to be present only during slow wave sleep (SWS). EEG exhibits random fractal structure with 1/f(-beta) spectrum (1 < beta < 3) and a negative linear correlation between D2 and beta in all states except during SWS. In consequence, in those states, finite D2 values could be attributed to the fractal nature of EEG and not to the presence of low-dimensional chaos, and therefore, it the use of beta would be more appropriate to describe the complexity of EEG, due to its lower computational cost.