  We investigate the nonclassicality of an open quantum system using
Leggett-Garg inequality (LGI) which test the correlations of a single system
measured at different times. Violation of LGI implies nonclassical behavior of
the open system. We investigate the violation of the Leggett-Garg inequality
for a two level system (qubit) spontaneously decaying under a general
non-Markovian dissipative environment. Our results are exact as we have
calculated the two-time correlation functions exactly for a wide range of
system-environment parameters beyond Born-Markov regime.
