The present paper identifies unique symmetry properties of the d→+d→d+p+n breakup reaction that make it an excellent probe for studying charge-symmetry breaking. Measurements were made for two configurations of the ejected particles in the breakup reaction to obtain values of the spin observables , , and . These observables are compared for the mirror reactions (d→,dp)n and (d→,dn)p for the two angle pairs (,,,)=(17.0°,0°,17.0°,180°) and (17.0°,0°,34.5°,180°) for an incident deutron energy of 12 MeV. In addition, spin observables for the (d→,pn)d reaction at = and =+180° are shown to provide a particularly good test of charge symmetry. Our , , and data for the (d→,pn)d reaction at (,,,)=(17.0°,0°,17.0°,180°) are used to illustrate this latter point. Of the ten charge-symmetric sets of observables measured, two were found to differ by 2.5 standard deviations.