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The high-resolution laser induced fluorescence spectrum of a molecular beam sample of calcium monohydride, CaH, in the region of the strongly overlapped (1,0) $A2\Pi -X2\Sigma +$ and $(0,0)B2\Sigma +\mathrm{<mrow\; data-mjx-texclass="ORD">-</mrow>}X2\Sigma +$ band systems near 630 nm and the $(0,0)A2\Pi -X2\Sigma +$ band system near 690 nm have been recorded and analyzed. The spectral features exhibit a small splitting which is attributed to proton magnetic hyperfine interactions in the $X2\Sigma +(v=0)$ $statea,b$. The energy levels of the $A2\Pi (v=0)$ and $X2\Sigma +(v=0)$ vibronic states were modeled using a traditional effective Hamiltonian approach, where as those for the interacting $A2\Pi (v=1)/B2\Sigma +(v=0)$ vibronic levels were modeled by augmenting the traditional effective Hamiltonian with terms to account for local perturbations. A comparison to the analysis of the high temperature spectra performed by $Martinc$, which did not include many of the spectral features of the present work, will be given.