  This paper deals with a "naive" way of generalization of the Kazhdan's
property (T) to C*-algebras. This approach differs from the approach of Connes
and Jones, which has already demonstrated its utility. Nevertheless it turned
out that our approach is applicable to the following rather subtle question in
the theory of C*-Hilbert modules.
  We prove that a separable unital C*-algebra A has property MI
(module-infinite, i.e., any C*-Hilbert module over A is self-dual if and only
if it is finitely generated projective) if and only if it has not property
(T1P) (property (T) at one point}, i.e. there exists in the unitary dual of A a
finite dimensional isolated point.
  The commutative case was studied in a previous paper.

Operator Algebras;Representation Theory