As far as i am certain of, i have only cadmium in my complex.
OK, if you're sure there is no metal impurity and you have it all covered, then the magnetism can only come from the ligand.
No need to describe the ligand entirely, but what about the group that is directly coordinated to the cadmium centre. What is it? Pyridine? Thiol?... You mentioned the ligand contain C, H, N and S. I wonder if you have something like that:
-C=C-
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HS SH
The cadmium being coordinated to the sulfur atoms. Do you have a group in your ligand that looks like that?
If so, there is possibility of a two-electron redox process similar to this one
http://en.wikipedia.org/wiki/File:1,2-benzoquinone_to_catechol.png (replace the oxygen atoms by sulfur ones). With a metal coordinating both sulfur atoms, a one electron redox process can occur, forming a radical.
The best characterisation method is definitely EPR. You would need to do some CV (cyclic voltammetry) as well if you have the double thiol-group I described above, in order to determine its redox potentials. And maybe some SQUID measurement if you think you have long-range magnetic order like anti-ferromagnetism,...