  We discuss constraints on soft CP-violating couplings of axion-like particles
with photon and fermions by using data on electric dipole moments of Standard
Model particles. In particular, for the ALP leptophilic scenario we derive
bounds on CP-odd ALP-photon-photon coupling from data of the {\tt ACME}
Collaboration on electron EDM. We also discuss prospects of the Storage Ring
experiment to constrain the ALP-photon-photon coupling from data on proton EDM
for the simplified hadrophilic interactions of ALP. The regarding constraints
from experimental bounds on the muon and neutron EDMs are weak. We set
constraint on the CP-odd ALP coupling with electron and derive bounds on
combinations of coupling constants, which involve soft CP-violating terms.
