A study of the associated production of a $\mathrm{Z} $ boson and a charm quark jet ( $\mathrm{Z} + \mathrm{c} $ ), and a comparison to production with a $\mathrm{b} $ quark jet ( $\mathrm{Z} + \mathrm{b} $ ), in $\mathrm {p}\mathrm {p}$ collisions at a centre-of-mass energy of 8 $,\text {TeV}$ are presented. The analysis uses a data sample corresponding to an integrated luminosity of 19.7 $,\text {fb}^{-1}$ , collected with the CMS detector at the CERN LHC. The $\mathrm{Z} $ boson candidates are identified through their decays into pairs of electrons or muons. Jets originating from heavy flavour quarks are identified using semileptonic decays of $\mathrm{c} $ or $\mathrm{b} $ flavoured hadrons and hadronic decays of charm hadrons. The measurements are performed in the kinematic region with two leptons with $p_{\mathrm {T}} ^{\ell } > 20,\text {GeV} $ , ${|\eta ^{\ell }|} < 2.1$ , $71< m_{\ell \ell } < 111,\text {GeV} $ , and heavy flavour jets with $p_{\mathrm {T}} ^{\text {jet}} > 25,\text {GeV} $ and ${|\eta ^{ \text {jet}}|} < 2.5$ . The $\mathrm{Z} + \mathrm{c} $ production cross section is measured to be $\sigma (\mathrm {p}\mathrm {p}\rightarrow \mathrm{Z} + \mathrm{c} + X) \mathcal {B}(\mathrm{Z} \rightarrow \ell ^+\ell ^-) = 8.8 \pm 0.5,\text {(stat)} \pm 0.6,\text {(syst)} ,\text {pb} $ . The ratio of the $\mathrm{Z} + \mathrm{c} $ and $\mathrm{Z} + \mathrm{b} $ production cross sections is measured to be $\sigma (\mathrm {p}\mathrm {p}\rightarrow \mathrm{Z} + \mathrm{c} + X)/\sigma (\mathrm {p}\mathrm {p}\rightarrow \mathrm{Z} + \mathrm{b} + X) = 2.0 \pm 0.2,\text {(stat)} \pm 0.2,\text {(syst)} $ . The $\mathrm{Z} + \mathrm{c} $ production cross section and the cross section ratio are also measured as a function of the transverse momentum of the $\mathrm{Z} $ boson and of the heavy flavour jet. The measurements are compared with theoretical predictions.