An aspect of the dynamical characterization of a system is its dimension, which can be used to infer the dynamical structure of the system. The correlation dimension (CorrD) is a measure of the dimensionality of the space occupied by a set of random points, often referred to as a type of fractal dimension. The aim of this study was to test the potential of CorrD in discriminating visual conditions (eyes open/closed) and groups (18 young and 17 older adults) from a raw and filtered center of pressure signal during a quiet stance position in medial-lateral and anterior-posterior directions. The subjects stood for 70 s on a level force plate operating at 100 Hz. The data were filtered by a fourth-order, zero-lag Butterworth filter with a cut-off frequency of 12.5 Hz. A mixed repeated measure ANOVA (eye vs. group) was applied, followed by a post-hoc test with Bonferroni correction. For raw data, significant greater CorrD was found for older adults for both medial-lateral and anterior-posterior COP sway in both eye conditions. No differences were found between eye conditions. For filtered data, significant greater CorrD was found for older adults only in the anterior-posterior direction for both eye conditions. A greater CorrD in eyes closed condition was found only for older adults and only in the anterior-posterior direction. The estimated values of CorrD are non-integer and below the superior bound, indicating a good CorrD estimation. The CorrD was greater for older adults in all significant situations, indicating the presence of a greater number of complex deterministic dynamics in the center of pressure sway for this group. The same can be inferred for the greater correlation dimension in the eyes-closed condition for this group. Finally, it is not clear if filtered or raw time-series produce more sensitive results.