The oxyfunctionalization of four centropolyindans, i.e., triptindan (2), 1,1’-(o-phenylene)-2,2’-spirobiindan (3), 10-methyltribenzoquinacene (4), and fenestrindan (5) at the benzylic and/or benzhydrylic C-H bonds of their rigid polycyclic framework has been achieved using dimethyldioxirane 1a and methyl(trifluoromethyl)dioxirane 1b. The latter reagent was found to be considerably more effective than 1a, allowing both partial and complete oxyfunctionalization of the substrates examined. The rigidity of the polycyclic framework and steric factors in 2-5 seem to moderate the reactivity and selectivity of the dioxiranes with respect to O-insertion into benzhydrylic vs benzylic C-H bonds; for instance in the oxyfunctionalization of the angular centrotriindan 3, the secondary benzylic alcohol 12 and the corresponding ketone 10 are obtained, along with the isomeric tertiary alcohol 11. The potentiality of 1b in effecting multiple oxygen insertion into C-H bonds under quite mild conditions was demonstrated by the remarkable high yield 4-fold hydroxylation of fenestrindan (5) at the bridgehead positions. The results are interpreted in terms of an essentially concerted O-insertion by the dioxirane into the C-H bonds encompassed in the rigid framework of the substrates. Adoption of an FMO model, which envisages dioxirane attack along the O-O bond axis toward the carbon atom of the given C-H bonds, provides a rationale for the reactivities and selectivities recorded.