  We find an analog of the electric-magnetic duality, which is a $Z_2$
transformation between magnetic and electric sectors of the static and
rotationally symmetric solutions in a class of (2+1)-dimensional
Einstein-Maxwell-Dilaton gravity theories. The theories in our consideration
include, in particular, one parameter class of theories continuously connecting
the Banados-Teitelboim-Zanelli (BTZ) gravity and the low energy string
effective theory. When there is no $U(1)$ charge, we have $O(2)$ or $O(1,1)$
symmetry, depending on a parameter that specifies each theory. Via the $Z_2$
transformation, we obtain exact magnetically charged solutions from the known
electrically charged solutions. We explain the relationship between the $Z_2$
transformation and $O(2,Z)$ symmetry, and comment on the $T$-duality of the
string theory.
