  Context. A proper estimate of the chromospheric magnetic fields is believed
to improve modelling of both active region and coronal mass ejection evolution.
Aims. We investigate the similarity between the chromospheric magnetic field
inferred from observations and the field obtained from a magnetohydrostatic
(MHS) extrapolation. Methods. Based Fe i 6173 {\AA} and Ca ii 8542 {\AA}
observations of NOAA active region 12723, we employed the spatially-regularised
weak-field approximation (WFA) to derive the vector magnetic field in the
chromosphere from Ca ii, as well as non-LTE inversions of Fe i and Ca ii to
infer a model atmosphere for selected regions. Milne-Eddington inversions of Fe
i serve as photospheric boundary for the MHS model that delivers the
three-dimensional field, gas pressure and density. Results. For the
line-of-sight component, the MHS chromospheric field generally agrees with the
non-LTE inversions and WFA, but tends to be weaker than those when larger in
magnitude than 300 G. The observationally inferred transverse component is
stronger, especially in magnetically weaker regions, yet the qualitative
distribution with height is similar to the MHS results. For either field
component the MHS chromospheric field lacks the fine structure derived from the
inversions. Furthermore, the MHS model does not recover the magnetic imprint
from a set of high fibrils connecting the main polarities. Conclusions. The MHS
extrapolation and WFA provide a qualitatively similar chromospheric field,
where the azimuth of the former is better aligned with Ca ii 8542 {\AA} fibrils
than that of the WFA, especially outside strong-field concentrations. The
amount of structure as well as the transverse field strengths are
underestimated by the MHS extrapolation. This underscores the importance of
considering a chromospheric magnetic field constraint in data-driven modelling
of active regions.
