A search is performed for charged-lepton flavor violating processes in top quark ((Formula presented)) production and decay. The data were collected by the CMS experiment from proton-proton collisions at a center-of-mass energy of 13 TeV and correspond to an integrated luminosity of (Formula presented). The selected events are required to contain one opposite-sign electron-muon pair, a third charged lepton (electron or muon), and at least one jet of which no more than one is associated with a bottom quark. Boosted decision trees are used to distinguish signal from background, exploiting differences in the kinematics of the final states particles. The data are consistent with the standard model expectation. Upper limits at 95% confidence level are placed in the context of effective field theory on the Wilson coefficients, which range between (Formula presented) depending on the flavor of the associated light quark and the Lorentz structure of the interaction. These limits are converted to upper limits on branching fractions involving up (charm) quarks, (Formula presented) ((Formula presented)), of (Formula presented), (Formula presented), and (Formula presented) for tensorlike, vectorlike, and scalarlike interactions, respectively.