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A search for the standard model Higgs boson decaying to a charm quark-antiquark pair, (Formula presented), produced in association with a top quark-antiquark pair ((Formula presented)) is presented. The search is performed with data from proton-proton collisions at (Formula presented), corresponding to an integrated luminosity of (Formula presented). Advanced machine learning techniques are employed for jet flavor identification and event classification. The Higgs boson decay to a bottom quark-antiquark pair is measured simultaneously and the observed (Formula presented) event rate relative to the standard model expectation is (Formula presented). The observed (expected) upper limit on the product of production cross section and branching fraction (Formula presented) is 0.11 (0.13) pb at 95% confidence level, corresponding to 7.8 (8.7) times the standard model prediction. When combined with the previous search for (Formula presented) via associated production with a (Formula presented) or (Formula presented) boson, the observed (expected) 95% confidence interval on the Higgs-charm Yukawa coupling modifier, (Formula presented), is (Formula presented) (2.7), the most stringent constraint to date.