  We report here the results of operation of a torsion balance with a period of
$\sim 1.27 \times 10^4$ s. The analysis of data collected over a period of
$\sim$115 days shows that the difference in the accelerations towards the
Galactic Center of test bodies made of aluminum and quartz was $(0.61 \pm 1.27)
\times 10^{-15} \, \mathrm{ m \, s}^{-2}$. This sets a bound on the violation
of the equivalence principle by forces exerted by Galactic dark matter which is
expressed by the E\"otv\"os parameter $\eta_{DM} = (1.32 \pm 2.68) \times
10^{-5}$, a significant improvement upon earlier bounds.
