  We report Spitzer Space Telescope IRAC 3.6, 4.5, 5.8 and 8 um and MIPS 24 and
70 um observations of the 32 Ori Group, a recently discovered nearby stellar
association situated towards northern Orion. The proximity of the group (~93
pc) has enabled a sensitive search for circumstellar dust around group members,
and its age (~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 um 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 um excesses, although the latter lacks 24 um
excess emission. The 24 um 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 um excesses among groups
lacking accreting T Tauri stars (behind only the approximately coeval 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_* values
for all the stars can be reasonably explained by steady state disk evolution.
