Results are presented from a search for charged-lepton flavor violating (CLFV) interactions in top quark production and decay in pp collisions at a center-of-mass energy of 13 TeV. The events are required to contain one oppositely charged electron-muon pair in the final state, along with at least one jet identified as originating from a bottom quark. The data correspond to an integrated luminosity of 138 fb^-1, collected by the CMS experiment at the LHC. This analysis includes both the production (q → eμt) and decay (t → eμq) modes of the top quark through CLFV interactions, with q referring to a u or c quark. These interactions are parametrized using an effective field theory approach. With no significant excess over the standard model expectation, the results are interpreted in terms of vector-, scalar-, and tensor-like CLFV four-fermion effective interactions. Finally, observed exclusion limits are set at 95% confidence levels on the respective branching fractions of a top quark to an eμ pair and an up (charm) quark of 0.13 × 10^-6 (1.31 × 10^-6), 0.07 × 10^-6 (0.89 × 10^-6), and 0.25 × 10^-6 (2.59 × 10^-6) for vector, scalar, and tensor CLFV interactions, respectively.