  We report an investigation of the superconducting properties of the hexagonal
noncentrosymmetric compound LaPdIn. Electrical resistivity, specific heat and
ac susceptibility measurements demonstrate the presence of bulk
superconductivity below $T_c$ = 1.6 K. The specific heat, together with the
penetration depth measured using transverse-field muon spin rotation and the
tunnel diode oscillator based method, are well described by single gap $s$-wave
superconductivity, with a gap magnitude of 1.8$k_BT_c$. From zero-field muon
spin relaxation results no evidence is found for the spontaneous emergence of
magnetic fields in the superconducting state, indicating that time-reversal
symmetry is preserved. Band structure calculations reveal that there is a
relatively weak effect of antisymmetric spin-orbit coupling on the electronic
bands near the Fermi level, which is consistent with there being negligible
singlet-triplet mixing due to broken inversion symmetry. On the other hand,
isostructural LuPdIn and LaPtIn do not exhibit superconductivity down to 0.4 K,
which may be due to these systems having a smaller density of states at the
Fermi level.
