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We give a sufficient condition for a $C^{\omega }$ (resp. $C^{\infty }$)-totally real, complex-tangential, $(n-1)$-dimensional submanifold in a weakly pseudoconvex boundary of class $C^{\omega }$ (resp. $C^{\infty }$) to be a local peak set for the class $𝒪$ (resp. $A^{\infty }$). Moreover, we give a consequence of it for Catlin’s multitype.