The INdias TIN (TIN.TIN) detector is under development in the search for neutrinoless double-β decay (0νββ) using 90% enriched 124 Sn isotope as the target mass. This detector will be housed in the upcoming underground facility of the India based Neutrino Observatory. We present the most important experimental parameters that would be used in the study of required sensitivity for the TIN.TIN experiment to probe the neutrino mass hierarchy. The sensitivity of the TIN.TIN detector in the presence of sole two neutrino double-β decay (2νββ) decay background is studied at various energy resolutions. The most optimistic and pessimistic scenario to probe the neutrino mass hierarchy at 3σ sensitivity level and 90% C.L. is also discussed.