From the canonical representation of the Marcum Q-function, a simple and highly accurate small argument approximation for the Marcum Q-function is first obtained. Utilizing this approximation, we derive the asymptotic error rate and outage probability expressions for multi-branch selection combining over generalized correlated Nakagami-m fading channels. These closed-form solutions can be used to provide rapid and accurate estimation of the error rates and outage probabilities in large signal-to-noise ratio regimes. It is shown that asymptotic error rates and outage probability over correlated Nakagami-m branches can be obtained by scaling the asymptotic error rates and outage probability over independent branches with a factor detm(M), where det(M) is the determinant of matrix M whose elements are the square root of the corresponding elements in the branch power covariance coefficient matrix.