A product and DFT computational study on the reactions of 3-ethyl-3-(trifluoromethyl)dioxirane (ETFDO) with bicyclic and spirocyclic hydrocarbons bearing cyclopropyl groups was carried out. With bicyclo[n.1.0]alkanes (n = 3-6), diastereoselective formation of the alcohol product derived from C2-H bond hydroxylation was observed, accompanied by smaller amounts of products derived from oxygenation at other sites. With 1-methylbicyclo[4.1.0]heptane, rearranged products were also observed in addition to the unrearranged products deriving from oxygenation at the most activated C2-H and C5-H bonds. With spiro[2.5]octane and 6-tert-butylspiro[2.5]octane, reaction with ETFDO occurred predominantly or exclusively at the axial C4-H to give unrearranged oxygenation products, accompanied by smaller amounts of rearranged bicyclo[4.2.0]octan-1-ols. The good to outstanding site-selectivities and diastereoselectivities are paralleled by the calculated activation free energies for the corresponding reaction pathways. Computations show that the σ* orbitals of the bicyclo[n.1.0]alkane cis or trans C2-H bonds and spiro[2.5]octanes axial C4-H bond hyperconjugatively interact with the Walsh orbitals of the cyclopropane ring, activating these bonds toward HAT to ETFDO. The detection of rearranged oxygenation products in the oxidation of 1-methylbicyclo[4.1.0]heptane, spiro[2.5]octane, and 6-tert-butylspiro[2.5]octane provides unambiguous evidence for the involvement of cationic intermediates in these reactions, representing the first examples on the operation of ET pathways in dioxirane-mediated C(sp3)-H bond oxygenations. Computations support these findings, showing that formation of cationic intermediates is associated with specific stabilizing hyperconjugative interactions between the incipient carbon radical and the cyclopropane C-C bonding orbitals that trigger ET to the incipient dioxirane derived 1,1,1-trifluoro-2-hydroxy-2-butoxyl radical.