Ultracold molecules with at least a metal centre generally have many interesting applications in quantum science and precision measurements . The heavy polar alkaline-earth metal monofluorides such as BaF and RaF have been identified as potential molecular systems for high-precision measurements to probe fundamental physics and many experimental as well as theoretical studies in this direction have been conducted on these molecules . It is worth to mention here that SrF, the lighter homologue of BaF and RaF is one of the most exciting diatomic molecules to be laser cooled . Thus, an accurate study of the P, T -odd effects of SrF with robust electronic structure methods could be helpful for experimental disentanglement of P, T -odd sources. Although a couple of investigations on SrF in search of P, T -odd effects are available in literature using quasi-relativistic theory and fully relativistic coupled-cluster-based methods , a detailed study of SrF employing more robust relativistic electronic structure theories would be helpful for future P, T -odd molecular experiments.Therefore, the aim of the present work is to perform such an electronic structure study of the lasercoolable SrF molecule by employing two analytic approaches, viz., Z-vector and linear expectation-value methods within the four-component relativistic coupled-cluster framework. We shall explore, in particular, the effects of basis set size, electron-correlation, relativity and nuclear model on the precise calculation of molecular-frame dipole moment and core-like properties such as the hyperfine structure coupling constants and the P, T -odd electronic structure parameters of the considered molecule in this work.