A search for a charged Higgs boson is performed with a data sample corresponding to an integrated luminosity of 19.7 $\pm$ 0.5 fb$^{-1}$ collected with the CMS detector in proton-proton collisions at $\sqrt{s} =$ 8 TeV. The charged Higgs boson is searched for in top quark decays for $m_{\mathrm{H}^\pm}$ lower then $m_{\mathrm t} - m_{\mathrm b}$, and in the direct production ${\rm pp \rightarrow t (b) H^\pm}$ for $m_{\mathrm H^\pm}$ larger than $m_{\mathrm t} - m_{\mathrm b}$. The ${\mathrm H^\pm\rightarrow \tau^\pm\nu_\tau}$ and ${\rm H^\pm\rightarrow t b}$ decay modes in the final states $\tau_{\rm h}$+jets, $\mu\tau_{\rm h}$, $\ell$+jets, and $\ell\ell$' ($\ell =$ e, $\mu$) are considered in the search. No signal is observed and 95% confidence level upper limits are set on the charged Higgs boson production. A model-independent upper limit on the product branching fraction \mathcal{B}({\rm t\rightarrow H^\pm b}) \, \mathcal{B}({\mathrm H^\pm \rightarrow \tau^\pm \nu_\tau})= 1.2-0.15% is obtained in the mass range $m_{\mathrm H^\pm} =$ 80-160 GeV, while the upper limit on the cross section times branching fraction \sigma({\rm pp \rightarrow t (b) H^\pm}) \, \mathcal{B} ({\mathrm H^\pm \rightarrow \tau^\pm \nu_\tau})= 0.38-0.025 pb is set in the mass range $m_{\mathrm H^+} =$ 180-600 GeV. Here, cross section $\sigma({\rm pp} \to {\rm t(b)H}^{\pm})$ stands for the sum $\sigma({\rm pp} \to \overline{\rm t}({\rm b}){\rm H}^{+}) + \sigma({\rm pp} \to {\rm t}(\overline{\rm b}){\rm H}^{-})$. Assuming $\mathcal{B}({\rm H}^\pm \rightarrow {\rm t b})=$ 1, an upper limit on $\sigma ({\rm pp} \rightarrow {\rm t} ({\rm b}) {\rm H}^\pm)$ of 2.0-0.13 pb is set for $m_{\mathrm H^\pm} =$ 180-600 GeV. The combination of all considered decay modes and final states is used to set exclusion limits in the $m_{\mathrm H^\pm}$-$\tan\beta$ parameter space in different MSSM benchmark scenarios.

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