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The present paper identifies unique symmetry properties of the [ital [rvec d]]+[ital d][r arrow][ital d]+[ital p]+[ital 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 [ital A][sub [ital y]], [ital A][sub [ital y][ital y]], and [ital A][sub [ital z][ital z]]. These observables are compared for the mirror reactions [sup 2]H([ital [rvec d]],[ital dp])[ital n] and [sup 2]H([ital [rvec d]],[ital dn])[ital p] for the two angle pairs ([theta][sub [ital d]],[phi][sub [ital d]],[theta][sub [ital N]],[phi][sub [ital N]])=(17.0[degree],0[degree],17.0[degree],180[degree]) and (17.0[degree],0[degree],34.5[degree],180[degree]) for an incident deutron energy of 12 MeV. In addition, spin observables for the [sup 2]H([ital [rvec d]],[ital pn])[ital d] reaction at [theta][sub [ital p]]=[theta][sub [ital n]] and [phi][sub [ital p]]=[phi][sub [ital n]]+180[degree] are shown to provide a particularly good test of charge symmetry. Our [ital A][sub [ital y]], [ital A][sub [ital y][ital y]], and [ital A][sub [ital z][ital z]] data for the [sup 2]H([ital [rvec d]],[ital pn])[ital d] reaction at ([theta][sub [ital p]],[phi][sub [ital p]],[theta][sub [ital n]],[phi][sub [ital n]])=(17.0[degree],0[degree],17.0[degree],180[degree]) are used to illustrate this latter point. Of the ten charge-symmetric sets of observables measured, two were foundmore » to differ by 2.5 standard deviations.« less more...