  In this note we comment on a recent attempt by P. Burikham, T. Harko, K.
Pimsamarn and S. Shahidi [Phys. Rev. D {\bf 107}, 064008 (2023)] to explain the
galactic rotation curves as the result of the motion of time-like test
particles in the Weyl geometric theory of gravity. We show that the static,
spherically symmetric solution found by the authors, which could be the basis
of an alternative explanation of the galactic rotation curves, is wrong.
