Spin point groups classify magnetic phases in the weak spin-orbit coupling regime and characterize the static properties of altermagnetic phases, but their dynamical consequences remain largely unexplored. Here, we derive selection rules for high-harmonic generation of charge and spin currents by extending dynamical symmetry to include spin point-group operations. Since spin currents transform under both real- and spin-space operations, whereas charge currents transform only under real-space operations, spin-current selection rules can reveal magnetic information that is inaccessible to charge-current harmonics. In a minimal altermagnetic model, an axis-aligned linearly polarized drive is nondiagnostic for distinguishing ferromagnetic and altermagnetic phases, although the antiferromagnetic phase is distinguished by the absence of the corresponding spin-current harmonics. A diagonal linearly polarized drive distinguishes the three spin-point-group phases within the weak-coupling spin-group description, whereas a single-helicity circularly polarized drive provides a sharper spin-current-harmonic criterion for distinguishing them from magnetic-point-group mimics. These results establish spin-current harmonics as a dynamical probe of spin-group symmetry. Finite spin-orbit coupling lifts these zeros only perturbatively: the forbidden harmonics acquire amplitudes analytic in the coupling strength, so that the fingerprint becomes a small same-order helicity contrast, below $3\times {10}^{-2}$ at low orders for couplings up to ${10}^{-2}$ of the hopping in our model.

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• Spin current
• Altermagnets
• High-harmonic generation