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SrF, being a laser-coolable molecule, can be an interesting system for spectroscopic tests of fundamental physics. We present an electronic structure study of this molecule within the four-component relativistic coupled-cluster singles and doubles (RCCSD) framework and employ the RCCSD-based methods to compute its molecular-frame dipole moment and core properties such as hyperfine structure coupling constant and molecular P, T-odd electronic structure parameters that are of great importance for the high-precision tests of fundamental physics. The impact of basis set size, Hamiltonian and nuclear model on the property calculation of SrF is also investigated. The computed results are in good agreement with the available experimental values. The present study shows that the SrF molecule could be useful for high-precision molecular experiments to explore physics beyond the Standard Model of elementary particles. [ABSTRACT FROM AUTHOR]