We report Spitzer Space Telescope IRAC 3.6 , 4.5 , 5.8 and 8 \mu m and MIPS 24 and 70 \mu m observations of the 32 Ori Group , a recently discovered nearby stellar association situated towards northern Orion . The proximity of the group ( \sim 93 pc ) has enabled a sensitive search for circumstellar dust around group members , and its age ( \sim 20 Myr ) corresponds roughly to an epoch thought to be important for terrestrial planet formation in our own solar system . We quantify infrared excess emission due to circumstellar dust among group members , utilizing available optical ( e.g . Hipparcos , Tycho ) and near-IR ( 2MASS ) photometry in addition to the Spitzer IR photometry . We report 4 out of the 14 objects which exhibit 24 \mu m excess emission more than 4 \sigma above the stellar photosphere ( > 20 % ) though lacking excess emission at shorter wavelengths : HD 35656 ( A0Vn ) , HD 36338 ( F4.5 ) , RX J0520.5+0616 ( K3 ) , and HD 35499 ( F4 ) . Two objects ( HD 35656 and RX J0520.0+0612 ) have 70 \mu m excesses , although the latter lacks 24 \mu m excess emission . The 24 \mu m disk fraction of this group is 29 ^ { +14 } _ { -9 } % , which is similar to previous findings for groups of comparable ages and places 32 Ori as the young stellar group with the 2nd most abundant 24 \mu m excesses among groups lacking accreting T Tauri stars ( behind only the approximately \beta Pic moving group ) . We also model the infrared excess emission using circumstellar dust disk models , placing constraints on disk parameters including L _ { IR } / L _ { * } , T _ { disk } , characteristic grain distance , and emitting area . The L _ { IR } / L _ { * } for all the stars can be reasonably explained by steady state disk evolution .