Increasing cognitive demand is accompanied by task-related cerebral hemodynamic changes but mean and variance alone may not describe their temporal organization. We assessed whether statistical complexity measures (SCM) derived from bilateral middle cerebral artery blood-velocity (CBv) signals varied across five arithmetic task levels in 26 healthy young adults (mean age 23.4 ± 2.1 years). Behavioral performance and NASA-TLX workload were also collected. For the primary Rényi configuration (embedding dimension m=7, alpha=1.4), SCM varied across baseline and task levels (Jensen-Rényi: Friedman chi-square=56.98, FDR-adjusted p=1.02x10-10, Kendall’s W=0.456; Jensen-Shannon: chi-square=70.23, FDR-adjusted p=3.66x10-13, W=0.562). Paired Wilcoxon tests with Holm correction identified differences for three of four adjacent task-level transitions (levels 2-3, 3-4, and 4-5), whereas levels 1-2 were not different. Conventional bilateral mean CBv also varied by level (chi-square=41.79, FDR-adjusted p=1.11x10-7, W=0.418). The mean of the recorded arterial-pressure channel did not differ after FDR correction (p=0.081), although its variance showed a small effect (W=0.110, FDR-adjusted p=0.032). These findings demonstrate that SCM provides a sensitive complementary characterization of task-related cerebral hemodynamic dynamics and supports its potential for scalable, within-person monitoring of graded cognitive demand.