  We investigate the violation of Leggett's inequality for non-local realism
using entangled coherent states and various types of local measurements. We
prove mathematically the relation between the violation of the
Clauser-Horne-Shimony-Holt form of Bell's inequality and Leggett's one when
tested by the same resources. For Leggett inequalities, we generalize the
non-local realistic bound to systems in Hilbert spaces larger than
bidimensional ones and introduce an optimization technique that allows to
achieve larger degrees of violation by adjusting the local measurement
settings. Our work describes the steps that should be performed to produce a
self-consistent generalization of Leggett's original arguments to
continuous-variable states.
