(1) Background: The influence of tap water fittings construction and internal pipe-work on the release of heavy metals was investigated. (2) Methods: A statistical approach was applied for the examination of the chemistry of tap water in five different cities in southern Poland. In total, 500 samples were collected (from 100 to 101 samples in each city). The sampling protocol included information on the construction of the water supply network and the physicochemical parameters of measured tap water. (3) Results: The statistical analysis allowed to extract the crucial factors that affect the concentrations of trace elements in tap water. Age of connection, age of tap, age of pipe-work as well as material of connection, material of pipe-work and material of appliance reveal the most significant variability of concentrations observed for As, Al, Cd, Cu, Fe, Mn, Pb, and Zn. Calculated cancer risks (CRs) decrease with the following order of analysed elements Ni > Cd > Cr > As = Pb and can be associated with the factors that affect the appearance of such elements in tap water. The hazard index (HI) was evaluated as negligible in 59.1% of the sampling points and low in 40.1% for adults. For children, a high risk was observed in 0.2%, medium in 9.0%, negligible in 0.4%, and low for the rest of the analysed samples.