In a recent experiment [Weinstein et al., Nature 395, 148 (1998)] we magnetically trapped 10(8) ground-state calcium monohydride molecules, CaH(X(2)Sigma,upsilon" = 0,J" = 0). The molecules were prepared by laser ablation of a solid sample of CaH2 and loaded via thermalization with a cold (< 1 K) He-3 buffer gas. The magnetic trap was formed by superconducting coils arranged in the anti-Helmholtz configuration. The detection was done by laser fluorescence spectroscopy excited at 635 nm (in the B (2)Sigma, upsilon＇ = 0 - X (2)Sigma, upsilon" = 0 band) and detected at 692 nm (within the B, upsilon＇ = 0 - X,upsilon" = 1 band ). Both a photomultiplier tube and a CCD camera were used. Due to the thermalization of molecular rotation, only a transition from the lowest rotational state could be detected at zero field, N＇ = 1,J＇ = 3/2 <--N" = 0,J" = 1/2. In the magnetic field this rotational transition splits into two features, one shifted towards lower and one towards higher frequencies. The measured shifts are linear in field strength and indicate a small difference (0.02 mu(B)) in the magnetic moments between the ground and excited states. Here we present a theoretical analysis of the observed magnetic shifts. These are identified as arising from a rotational perturbation of the B (2)Sigma,upsilon＇ = 0 state by a close-lying A (2)Pi,upsilon＇ = 1 state that lends the B state some of its A character. We find that the Hamiltonian can be well approximated by a 3 x 3 matrix built out of elements that connect states from within the Sigma-doublet and the (2)Pi(3/2) manifolds. The interaction parameter describing the Sigma-Pi coupling in the Zeeman Hamiltonian is determined from the observed shifts and the field-free molecular parameters of CaH given by Berg and Klyning [Phys. Scr. 10, 331 (1974)] and by Martin [J. Mol. Spectrosc 108, 66 (1984)].