Using a combination of first-principles density functional theory (DFT) calculations and exact diagonalization studies of a first-principles derived model, we carry out a microscopic analysis of the magnetic properties of the half-metallic double perovskite compound, Sr2CrMoO6, a sister compound of the much discussed material Sr2FeMoO6. The electronic structure of Sr2CrMoO6, though appears similar to Sr2FeMoO6 at first glance, shows non trivial differences with that of Sr2FeMoO6 on closer examination. In this context, our study highlights the importance of charge transfer energy between the two transition metal sites. The change in charge transfer energy due to shift of Cr d states in Sr2CrMoO6 compared to Fe d in Sr2FeMoO6 suppresses the hybridization between Cr t2g and Mo t2g. This strongly weakens the hybridization-driven mechanism of magnetism discussed for Sr2FeMoO6. Our study reveals that, nonetheless, the magnetic transition temperature of Sr2CrMoO6 remains high since additional superexchange contribution to magnetism arises with a finite intrinsic moment developed at the Mo site. We further discuss the situation in comparison to another related double perovskite compound, Sr2CrWO6. We also examine the effect of correlation beyond DFT, using dynamical mean field theory (DMFT).