  We present a magneto-optical study of individual self-assembled CdSe/ZnSe
quantum dots doped with single Mn$^{2+}$ ions. Properties of the studied dots
are analyzed analogously to more explored system of Mn-doped CdTe/ZnTe dots.
Characteristic sixfold splitting of the neutral exciton emission line as well
as its evolution in the magnetic field are described using a spin Hamiltonian
model. Dynamics of both exciton recombination and Mn$^{2+}$ spin relaxation are
extracted from a series of time-resolved experiments. Presence of a single
dopant is shown not to affect the average excitonic lifetime measured for a
number of nonmagnetic and Mn-doped dots. On the other hand, non-resonant
pumping is demonstrated to depolarize the Mn$^{2+}$ spin in a quantum dot
placed in external magnetic field. This effect is utilized to determine the ion
spin relaxation time in the dark.
