A search for a standard model Higgs boson produced in association with a top-quark pair and decaying to bottom quarks is presented. Events with hadronic jets and one or two oppositely charged leptons are selected from a data sample corresponding to an integrated luminosity of 19.5 $,\text {fb}^\text {-1}$ collected by the CMS experiment at the LHC in $\mathrm {p}\mathrm {p}$ collisions at a centre-of-mass energy of 8 $,\hbox {TeV}$ . In order to separate the signal from the larger $\hbox {t}\overline{\hbox {t}}$  + jets background, this analysis uses a matrix element method that assigns a probability density value to each reconstructed event under signal or background hypotheses. The ratio between the two values is used in a maximum likelihood fit to extract the signal yield. The results are presented in terms of the measured signal strength modifier, $\mu $ , relative to the standard model prediction for a Higgs boson mass of 125 $,\hbox {GeV}$ . The observed (expected) exclusion limit at a 95 % confidence level is $\mu <4.2$ (3.3), corresponding to a best fit value $\hat{\mu }=1.2^{+1.6-1.5}$ .