We report the measurement of the non-reactor environmental backgrounds and the detector response with the Indian Scintillator Matrix for Reactor Anti-Neutrinos (ISMRAN), which is $\sim$1 ton detector setup by volume, consisting of 10$\times$9 (10 rows and 9 columns) Plastic Scintillator Bars (PSBs) array at BARC, Mumbai, India. ISMRAN is an above-ground anti-neutrino (${\overline{{\nu}}_{e}}$) experiment at very short baseline located at Dhruva research reactor facility. It is enclosed by a shielding made of 10 cm thick lead and 10 cm thick borated polyethylene to minimize the backgrounds and is mounted on a movable base structure, situated at $\sim$ 13 m away from the reactor core. These measurements are useful in the context of the ISMRAN detector setup that will be used to detect the reactor ${\overline{{\nu}}_{e}}$ and measure its energy spectrum through the inverse beta decay (IBD) process. In this paper, we present the energy resolution model and energy non-linearity model of PSB and the cosmogenic muon-induced background, based on the sum of their energy depositions and number of hit bars. Reconstructed sum energy spectrum and number of hit bars distribution for $\mathrm{{}^{22}Na}$ radioactive source has been compared with Geant4 based Monte Carlo simulations. These experimentally measured results will be useful for discriminating the correlated and uncorrelated background events from the true IBD events in reactor ON and OFF conditions inside the reactor hall.