A search for flavor-changing neutral currents (FCNC) in associated production of a top quark with a Higgs boson is presented. Two channels are considered: top quark pair production, with FCNC decay of the top quark or antiquark, and single top production ($pp \to tH$). This is the first analysis to probe top-Higgs FCNC couplings in the single top production mode. A final state with one isolated lepton and at least three reconstructed jets, among which at least two are identified as b quark jets, is studied. The data sample corresponds to an integrated luminosity of 35.9~\mathrm{fb}^{-1} recorded by the CMS experiment at the LHC in proton-proton collisions at \sqrt{s}=13~\mathrm{TeV} in 2016. No significant deviation is observed from predicted background. Observed (expected) upper limits at $95\%$ confidence level are set on the branching ratios of top quark decays, B(t \rightarrow u H) < 0.47\%~(0.34\%) and B(t \rightarrow c H) < 0.47\%~(0.44\%), assuming a single non-vanishing FCNC coupling.

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