  In the present investigation, we evaluate the in-medium partial decay widths
of exited states $\psi$(4040) and $Y$(4008) decaying to the pairs of
non-strange pseudoscalar $D \bar{D}$ mesons, strange pseudoscalar $D_s
\bar{D}_s$ mesons, non-strange vector $D^* \bar{D}^*$ meson and
pseudoscalar-vector $D \bar{D}^*$ mesons using $^3P_0$ model. The in-medium
effects are incorporated through the in-medium masses of daughter mesons
(calculated using the chiral SU(3) model and QCD sum rule approach in our
previous works). We consider $\psi$(4040) and $Y$(4008) states as 3$^3S_1$
states and observe the in-medium dominance of one state over the other for a
given decay mode. The results of the present investigation will prove as one
step forward in assigning the correct spectroscopic state to controversial
$Y$(4008) state.
