Theoretical developments on selection combiner output (SCO) multivariate distributions of popular correlated fading environments, such as Rayleigh, Rician, and Nakagami-m, have been studied in the literature, but those of generalized-Rician fading have not been rigorously studied. The generalized-Rician fading environment, comprising of n underlying non-zero mean independent and identically distributed Gaussian random variables, can be generalized to Rayleigh, Rician, and Nakagami-m fading. In addition, available findings on this topic in the open literature are scattered with mathematical mistakes. This letter thus derives SCO correlated generalized-Rician multivariate cumulative distribution function, then identifies mathematical errors in the open literature, and corrects them. Cross verification of well-known results is mathematically employed. Simulation details of average bit error rate for binary frequency-shift keying are also given for verification purposes.