We estimate the stable rank  of residually finite dimensional 
$C^*$-algebras  by that of the $C^*$-algebras of continuous 
fields associated with their (continuous) separating, 
finite dimensional irreducible representations.
Moreover, as the main application we estimate the stable rank, 
connected stable rank and real rank of reduced group $C^*$-algebras 
of residually finite, discrete groups with the property (T).