  This paper presents a spectral and photometric study of the poorly studied
polar BM CrB. Three states of the polar brightness and signs of transition from
one-pole to two-pole accretion mode were found by an analysis of ZTF data. It
is shown that the transition from the low state to the high state changes the
longitude of the main accretion spot (by $\approx 17^{\circ}$) and increases
its elongation (by $\approx 10^{\circ}$). The spectra contain Zeeman
absorptions of the H$\alpha$ line which are formed at a magnetic field strength
of $15.5\pm1$ MG. These absorptions are likely produced by a cold halo
extending from the accretion spot at $\approx {^1/_4}$ of the white dwarf
radius. Modeling of the behavior of the H$\alpha$ emission line shows that the
main source of emission is the part of the accretion stream near the Lagrangian
point L$_1$, which is periodically eclipsed by the donor star. The spectra
exhibit a cyclotron component formed in the accretion spot. Its modeling by a
simple accretion spot model gives constraints on the magnetic field strength
$B=15-40$ MG and the temperature $T_e\gtrsim15$ keV.
