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Molecular predissociation, the spontaneous nonradiative bond-breaking process, can limit the ability to scatter a large number of photons required to reach the ultracold regime in laser cooling. Unlike rovibrational branching, predissociation is irreversible since the fragments fly apart with high kinetic energy. Of particular interest is the simple diatomic molecule CaH, for which the two lowest electronically excited states used in laser cooling, A^{2}Π_{1/2} and B^{2}Σ^{+}, lie above the dissociation threshold of the ground potential. In this work, we present measurements and calculations that quantify the predissociation probabilities P_{pd} affecting the cooling cycle. For the lowest vibrational levels, we find P_{pd} of ∼10^{−6} for A(v^{′}=0) and ∼10^{−3} for B(v^{′}=0). The results allow us to design a laser-cooling scheme that will enable the creation of an ultracold and optically trapped cloud of CaH molecules. In addition, we use the results to propose a two-photon pathway to controlled dissociation of the molecules in order to gain access to their ultracold fragments, including hydrogen.