The 2nd isomeric state of 178Hf has high energy of 2.446 MeV, and big half-life of 31 yr related to its high spin 16+. Normally it decays spontaneously to the ground state of 178Hf by isomeric transition with emission of cascade of gamma quanta with energies up to ~600 keV. Possible interactions of 178m2Hf with some given inelastic Dark Matter (iDM) candidates could lead to emission of gamma rays with higher energies (>1 MeV) from the excited levels of 178Hf which are not populated in its usual decay. The search for such gamma rays was performed deep underground at the Gran Sasso National Laboratory of the INFN in measurements of 178m2Hf source with an activity of ~63 Bq with two ultra-low-background HPGe gamma spectrometers over cumulative 1170 h. This is the first 178m2Hf measurements in the low-background conditions which allowed the enhancement of the sensitivity - in the framework of the models considered here - to hypothesized iDM induced decay at energies >600 keV thanks to reduced natural radioactive background. Improved half-life limits for several hypothesized iDM induced transitions were set, up to the level of lim T1/2 > 10^7 yr, higher (or competitive) than those known previously.