Predicting flow in fractured reservoirs remains challenging as it highly depends on hydraulic connectivity of fractures which can vary from point to point. Classical pumping experiments conducted in fractured reservoirs often display fractional flow and anomalous slow diffusion due to bottlenecks or dead zones, characteristic of heterogeneity. In order to investigate reservoir properties at a contaminated site in the Simi Hills (South California, USA), composed by sandstones (dominant calcite cement) inter-bedded with fine-grained formations (shales, siltstones and mudstones), a large scale pumping test was performed in a major fault over 151 days. Deconvolution was applied first to remove the effect of variable flow rates and obtain constant-rate responses of the reservoir. Next, pressure-transients were analyzed both in time and space to get flow dimension, n, through the pressure derivative and extract the anomalous diffusion exponent, dw, as well as the fractal dimension, df. Analysis revealed at least two kinds of responses characterized by flow dimensions of 0.08 and 0.39 and anomalous diffusion exponents of 2.16 and 2.93, respectively. These properties, which can be related to major geological structures (i.e. major faults and surrounding fractures network), shows decreasing hydraulic properties (transmissivity, T, and storativity, S), and consequently, decreasing hydraulic connectivity, with increasing scale of investigation. In particular, the major fault (n = 0.39 ; dw = 2.93) shows a relationship of about T~S3 with T~r-1.36 and S~r-0.43, consistent with flow within a fracture, while the surrounding fractures network (n = 0.08 ; dw = 2.16) displays a relationship which follow T~S with T~r-1.07 and S~r-0.91. This scale-dependence of hydraulic properties may help improve groundwater flow prediction in such fractured reservoirs and could be taken into account for long-term transport of contaminants at this site.