  To a complex reflection arrangement with an invariant multiplicity function
one can relate the space of logarithmic vector fields and the space of
quasi-invariants, which are both modules over invariant polynomials. We
establish a close relation between these modules. Berest-Chalykh freeness
results for the module of quasi-invariants lead to new free complex reflection
multiarrangements. K. Saito's primitive derivative gives a linear map between
certain spaces of quasi-invariants.
  We also establish a close relation between non-homogeneous quasi-invariants
for root systems and logarithmic vector fields for the extended Catalan
arrangements. As an application, we prove the freeness of Catalan arrangements
corresponding to the non-reduced root system $BC_N$.
