We propose a symmetry resolution of entanglement for categorical noninvertible symmetries (CaT-SREE) in (1+1)-dimensional conformal field theories. The definition parallels that of grouplike invertible symmetries, employing the concept of symmetric boundary states with respect to a categorical symmetry. Our examination extends to rational conformal field theories, where the behavior of CaT-SREE mirrors that of grouplike invertible symmetries. We find that CaT-SREE can be defined if there is no obstruction to gauging the categorical symmetry, as happens in the case of grouplike symmetries. We also provide instances of the breakdown of entanglement equipartition at the next-to-leading order in the cutoff expansion. Our findings shed light on how the interplay between conformal boundary conditions and categorical symmetries lead to specific patterns in the entanglement entropy. Published by the American Physical Society 2024