jats:titleAbstract</jats:title>jats:pCosmic ray (CR) interactions can be a challenging source of background for neutrino oscillation and cross-section measurements in surface detectors. We present methods for CR rejection in measurements of charged-current quasielastic-like (CCQE-like) neutrino interactions, with a muon and a proton in the final state, measured using liquid argon time projection chambers (LArTPCs). Using a sample of cosmic data collected with the MicroBooNE detector, mixed with simulated neutrino scattering events, a set of event selection criteria is developed that produces an event sample with minimal contribution from CR background. Depending on the selection criteria used a purity between 50 and 80% can be achieved with a signal selection efficiency between 50 and 25%, with higher purity coming at the expense of lower efficiency. While using a specific dataset and selection criteria values optimized for the MicroBooNE detector, the concepts presented here are generic and can be adapted for various studies of exclusive jats:inline-formulajats:alternativesjats:tex-math$$\nu _{\mu }$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msub mml:miν</mml:mi> mml:miμ</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula> CCQE interactions in LArTPCs.</jats:p>