  We reveal that three-dimensional multi-orbital topological superconductivity
can be identified by a bulk measurement, i.e., the temperature dependence of
nuclear magnetic relaxation (NMR) rates. Below a critical temperature $T_{\rm
c}$, the NMR rate in the topological state exhibits an anti-peak profile, which
is opposite to the conventional $s$-wave state. This inversion coherence effect
comes from a twist of order parameters with respect to orbital and spin degrees
of freedom. Our self-consistent calculations in the model for
Cu$_{x}$Bi$_{2}$Se$_{3}$ prove that the inverse coherence effect appears as a
concave temperature dependence of the NMR rates. We propose that a
time-reversal-invariant orbital-singlet spin-triplet topological
superconductivity is characterized by the temperature dependence of the NMR
rate.
