  We present a complete calculation of the next-to-next-to-leading (NNLO)
electroweak corrections involving closed fermion loops to the $e^+ e^- \to ZH$
process. This has been achieved by using a semi-numerical technique for the
two-loop vertex and box diagrams, which is based on Feynman parameters and
dispersion relations for one of the two sub-loops. UV divergences are treated
with suitable subtraction terms. Numerical results for the unpolarized
differential and integrated cross-section at center-of-mass energy
$\sqrt{s}=240~\text{GeV}$ are provided. Combining the NNLO contributions with
one and two closed fermions loops, they are found to increase the NLO
cross-section by 0.7\%.
