Polycrystalline samples of InMnO3, prepared by decomposition of nitrates, were found to be isostructural with LuMuO3 rather than YAIO3 as was the case for flux-grown InMnO3 single crystals. The structure was refined in P63cm from powder neutron data with a = 5.8758(4) Å and c = 11.4715(8) Å at 293 K. Single crystals of ScMnO3 were grown from a PbF2 flux. The structure was refined from single crystal X-ray data also in P63cm with a = 5.8286(6) Å and c = 11.1738(9) Å. Magnetic susceptibility data for InMnO3 show subtle anomalies near 120 and 40 K and a weak maximum at 15 K for applied fields <0.05 T. Neutron diffraction data reveal a complex structure with two distinct classes of reflections. From 295 to 5 K, a broad (100) reflection is seen which is well described by a Warren-type lineshape and which is assigned to two-dimensional in-plane Mn-Mn spin correlations. Below 120 K, reflections indexed as (h 0 n/2) and (h 1 n /2) appear which exhibit an unusual temperature dependence featuring intensity maxima near 60-70 K and which are significantly broader than the resolution limit at all temperatures. These are assigned to correlations between spin-coupled Mn layers, also of short range. The absence of long-range order in InMnO3 is contrasted with the well-established order in isostructural ScMnO3 and LnMnO3. It is argued that the differences can be rationalized in terms of an anomalously long c-axis for InMnO3 which leads to a weakening of key interlayer superexchange pathways necessary for the realization of long-range order. This situation is also discussed in terms of recent mean-field theory for layered antiferromagnets.