Computer-based numerical simulations of the cardiac electrophysiology (EP) and relative clinical outputs such as the electrocardiograms (ECGs) can play an important role in understanding heart diseases. The ECG can be mathematically modelled by a large parameter-dependent coupled non-linear dynamical system, on different and rather involved domains, usually solved by employing finite element (FE) schemes [1]. The computational efficiency of such expensive problem poses one of the major challenges, especially when considering realistic heart and human torso. Moreover, the ECG is very sensitive to small variations of the model parameters, which makes the efficiency issues even more important. In this work, following [2], we propose a parametric reduced order model (ROM) for one-way heart-torso coupled problems able to efficiently reproduce ECGs. We therefore aim at reducing the computational burden of solving the Bidomain model coupled with a Laplace problem in a human torso. We employ RB techniques on each sub-problems, and the DEIM to handle the parameter dependent data across the conforming, or non-conforming, meshes at the domains interface. Main result of this work is the reduction of the computational costs of solving EP segregated heart-torso problems (i) featuring interface non-conformity, (ii) through the application of RB schemes, on realistic domains. [1] M. Boulakia, S. Cazeu, M.A. Fern´andez, J.F. Gerbeau, N. Zenzemi, Mathematical Modeling of Electrocardiograms: A Numerical Study. Ann Biomed Eng, Vol. 38, pp. 1071--1097, 2010. [2] E. Zappon, A. Manzoni, A. Quarteroni, Efficient and certified solution of parametrized one-way coupled problems through DEIM-based data projection across non-conforming interfaces. Adv Comput Math, Vol. 49, 2023.