We have performed a relativistic coupled-cluster study of moderately heavy laser-coolable SrF molecule to investigate the effects of electron-correlation, basis set size, Hamiltonian and nuclear model on the computation of its firstorder properties-the molecular-frame dipole moment, the HFS constant and the P, T -violating electronic structure parameters. Our study shows that the X2C Hamiltonian has reproduced the four-component results for the core properties of SrF within 3.5% uncertainty. The results computed using the point nuclear model are in very good agreement with the finite-size nuclei (modelled by the Gaussian charge distribution) results except in the case of the S-PS interaction parameter. In conclusion, the P, T -odd molecular parameters of SrF are large and thus it could be an important system for high precision molecular experiments to probe fundamental physics.