  We study the Morita equivalence for field theories on noncommutative
two-tori. For rational values of the noncommutativity parameter $\theta $ (in
appropriate units) we show the equivalence between an abelian noncommutative
field theory and a nonabelian theory of twisted fields on ordinary space. We
concentrate on a particular conformal field theory (CFT), the one obtained by
means of the m-reduction procedure (V. Marotta, J. Phys. A 26 (1993) 3481; Mod.
Phys. Lett. A 13 (1998) 853; Nucl. Phys. B 527 (1998) 717), and show that the
Morita equivalence also holds at this level. An application to the physics of a
quantum Hall fluid at Jain fillings \nu =m/2pm+1 is explicitly considered in
order to further elucidate such a correspondence.
