  If ultra-light dark matter (ULDM) exists and couples to neutrinos, it can be
discovered via time-periodic variations in the neutrino mass and mixing
parameters. We analyze the current bounds on such a scenario and establish the
sensitivity expected for both time-averaged and time-resolved modulations in
future neutrino oscillation experiments. We place a special emphasis in our
analysis on time modulations of the CP violating mixing phase. We illustrate
with a toy model the case where the leading modulation effect can be CP
violating while the effect on CP conserving parameters is suppressed. We show a
unique imprint that a time averaged CP violating modulation of ULDM can leave
in neutrino oscillations, while direct CP asymmetries vanish.
