  The pairing symmetry of the hexagonal pnictide superconductor SrPtAs is
discussed with taking into account its multiband structure. The topological
chiral $d$-wave state with time-reversal-symmetry breaking has been anticipated
from the spontaneous magnetization observed by the muon-spin-relaxation
experiment. We point out in this paper that the recent experimental reports on
the nuclear-spin-lattice relaxation rate $T_1^{-1}$ and superfluid density
$n_s(T)$, which seemingly support the conventional $s$-wave pairing, are also
consistent with the chiral $d$-wave state. The compatibility of the gap and
multiband structures is crucial in this argument. We propose that the
measurement of the bulk quasiparticle density of states would be useful for the
distinction between two pairing states.
