  We show that the distribution of bulk spacings between pairs of adjacent
eigenvalue real parts of a random matrix drawn from the complex elliptic
Ginibre ensemble is asymptotically given by a generalization of the
Gaudin-Mehta distribution, in the limit of weak non-Hermiticity. The same
generalization is expressed in terms of an integro-differential Painlev\'e
function and it is shown that the generalized Gaudin-Mehta distribution
describes the crossover, with increasing degree of non-Hermiticity, from
Gaudin-Mehta nearest-neighbor bulk statistics in the Gaussian Unitary Ensemble
to Poisson gap statistics for eigenvalue real parts in the bulk of the Complex
Ginibre Ensemble.
