In this note the author gives a conceptual and simpler proof of some of \n J.-M. Ku's\en results [J. Algebra {\bf 106} (1987), no. 2, 403--412; MR0880965 (88e:17023)] on the structure of local modules in the category $\scr O$ of Kac-Moody algebras by making use of projective module theory.