Supernova remnants (SNRs) interacting with molecular clouds are potentially exciting systems in which to detect evidence of cosmic ray acceleration. Prominent γ-ray emission is produced via the decay of neutral pions when cosmic rays encounter nearby dense clouds. In many of the SNRs coincident with γ-ray sources, the presence of OH (1720 MHz) masers is used to identify interaction with dense gas and to provide a kinematic distance to the system. In this Letter we use statistical tests to demonstrate that there is a correlation between these masers and a class of GeV- to TeV-energy γ-ray sources coincident with interacting remnants. For pion decay the γ-ray luminosity provides a direct estimate of the local cosmic ray density. We find the cosmic ray density is enhanced by one to two orders of magnitude over the local solar value, comparable to X-ray-induced ionization in these remnants. The inferred ionization rates are sufficient to explain non-equilibrium chemistry in the post-shock gas, where high columns of hydroxyl are observed.