We present the physical parameters of 2335 late-type contact binary (CB) systems extracted from the Catalina Sky Survey (CSS). Our sample was selected from the CSS Data Release 1 by strictly limiting the prevailing temperature uncertainties and light-curve fitting residuals, allowing us to almost eliminate any possible contaminants. We developed an automatic Wilson–Devinney-type code to derive the relative properties of CBs based on their light-curve morphology. By adopting the distances derived from CB (orbital) period–luminosity relations (PLRs), combined with the well-defined mass–luminosity relation for the systems' primary stars and assuming solar metallicity, we calculated the objects' masses, radii, and luminosities. Our sample of fully eclipsing CBs contains 1530 W-, 710 A-, and 95 B-type CBs. A comparison with literature data and with the results from different surveys confirms the accuracy and coherence of our measurements. The period distributions of the various CB subtypes are different, hinting at a possible evolutionary sequence. W-type CBs are clearly located in a strip in the total mass versus mass-ratio plane, while A-type CBs may exhibit a slightly different dependence. There are no significant differences among the PLRs of A- and W-type CBs, but the PLR zero-points are affected by their mass ratios and fill-out factors. Determination of zero-point differences for different types of CBs may help us improve the accuracy of the resulting PLRs. We demonstrate that automated approaches to deriving CB properties could be a powerful tool for application to the much larger CB samples expected to result from future surveys.