We present long-range statistical properties of a recently introduced unitary random matrix ensemble, whose short-range correlations were found to describe a transition from Wigner to Poisson-type as a function of a single parameter. We argue, by evaluating the two-level correlation function of a different solvable model, that the transition is perhaps a quite general feature for a class of models. Our analytic results compare well with numerical studies on a variety of physical systems. We discuss the possibility of observing experimentally the signature of such transitions.