A search for the production of a Higgs boson in association with a single top quark is presented, focusing on leptonic signatures provided by the $\mathrm{H}\rightarrow\mathrm{W}\mathrm{W}$, $\mathrm{H}\rightarrow\tau\tau$, and $\mathrm{H}\rightarrow\mathrm{Z}\mathrm{Z}$ decay modes. Due to strong interference of the two main leading-order diagrams, the production cross section of this process is highly sensitive to the relative sign of the top-Higgs coupling modifier, $\kappa_{\mathrm{t}}$, and the coupling modifier of vector bosons to the Higgs, $\kappa_{\mathrm{V}}$. The analysis exploits signatures with two same-sign leptons or three leptons in the final state, and uses the 2016 data sample collected with the CMS detector at the LHC at a center of mass energy of 13~\mathrm{TeV}, which corresponds to an integrated luminosity of 35.9~\mathrm{fb}^{-1}. Multivariate techniques are used to discriminate the signal from the dominant backgrounds. The analysis yields a $95\%$ confidence level (C.L.) upper limit on the combined $\mathrm{tH}+\mathrm{t\overline{t}H}$ production cross section times branching ratio of 0.64\,\mathrm{pb}, with an expected limit of 0.32\,\mathrm{pb}, for a scenario with $\kappa_\mathrm{t}=-1.0$ and $\kappa_\mathrm{V}=1.0$. Values of $\kappa_\mathrm{t}$ outside the range of $-1.25$ to $+1.60$ are excluded at $95\%$ C.L., assuming $\kappa_\mathrm{V}=1.0$.

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