A search is presented for the production of a Higgs boson in association with a single top quark, based on data collected in 2016 by the CMS experiment at the LHC at a center-of-mass energy of 13 TeV, which corresponds to an integrated luminosity of 35.9 fb$^{-1}$ . The production cross section for this process is highly sensitive to the absolute values of the top quark Yukawa coupling, ${y_\mathrm{t}}$, the Higgs boson coupling to vector bosons, ${g_{\mathrm{H}\mathrm{VV}}}$, and, uniquely, to their relative sign. Analyses using multilepton signatures, targeting $\mathrm{H}\to\mathrm{W}\mathrm{W}$, $\mathrm{H}\to\tau\tau$, and $\mathrm{H}\to\mathrm{Z}\mathrm{Z}$ decay modes, and signatures with a single lepton and a $\mathrm{b\bar{b}}$ pair, targeting the $\mathrm{H}\to\mathrm{b\bar{b}}$ decay, are combined with a reinterpretation of a measurement in the $\mathrm{H}\to{\gamma\gamma}$ channel to constrain ${y_\mathrm{t}}$. For a standard model-like value of ${g_{\mathrm{H}\mathrm{VV}}}$, the data favor positive values of ${y_\mathrm{t}}$ and exclude values of ${y_\mathrm{t}}$ below about -0.9\,{y_\mathrm{t}} ^\mathrm{SM}.

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