Superconductivity in a nitride of the MAX-phase family was reported by A.D. Bortolozo et al. in Ti2InN (a = 0.3074 nm, c = 1.3975 nm) with a transition temperature of 7.3 K. In this study, we report on Ti2InN MAX phase-based samples (with up to 94 wt.% of Ti2InN) synthesized by several methods, which, unfortunately, did not comply with bulk superconductivity of this compound. The Ti2InN materials were synthesized from Ti2InN precursor powder of 93-95 wt.% purity (obtained by the method proposed by (Bortolozo et al., 2010)) according to the following routes: (1) at 130 bar of N2, leading to 54 wt.% of Ti2InN (a = 0.3076(1), c = 1.4012(5) nm); (2) in a sealed quartz ampoule in Ar, (88.5 wt.% Ti2InN, a = 0.3076(1), c = 1.4012(4) nm); (3) by spark plasma sintering (SPS) in contact with hBN at 45 MPa (94 wt.% Ti2InN, a = 0.3077(7), c = 1.4021(5) nm), and (4) by high quasihydrostatic pressure - high temperature sintering (HP-HT) in contact with hBN at 4 GPa (83.5 wt.% Ti2InN, a = 0.3075(3), c = 1.4017(5) nm). Despite all the manufactured samples demonstrated superconducting behaviour with Tc (onset) near 5 K and the samples prepared by SPS and HP-HT methods were highly dense, a very broad magnetic transition (ac susceptibility) not saturating down to 2 K has been observed. No macroscopic Meissner phase was established and the magnetization was far too weak to evidence bulk superconductivity of the entire sample and hence of Ti2InN. However, a superconducting gap of about 1.2-2.1 mV was derived from point-contact spectroscopy at some areas of HP-HT sintered samples. The dispersed crystalline admixture grains of TiN phase in Ti2InN matrices of our samples or a metallic In-alloy are most probable candidates for the superconducting phase in our materials.