Lets take two-atomic molecule that has spin while the both atoms have zero spin. Can we choose a frame of reference where this molecule has no spin?
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Possibly helpful: http://physics.stackexchange.com/questions/23517/how-to-find-that-a-molecule-has-zero-spin – Carl Witthoft Oct 10 '14 at 12:31
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Spin is precisely the number that tells you in which representation of the rotation group $\mathrm{SO}(3)$ (non-relativistic) or Lorentz group $\mathrm{SO}(1,3)$ (relativistic) a quantum state transforms. As these groups are precisely the transformations between reference frames (aside from the boring translations), spin is an invariant under change of reference frame.
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