We explore the relationships between the 3.3 \micron polycyclic aromatic hydrocarbon ( PAH ) feature and active galactic nucleus ( AGN ) properties of a sample of 54 hard X-­ray selected bright AGNs , including both Seyfert 1 and Seyfert 2 type objects , using the InfraRed Camera ( IRC ) on board the infrared astronomical satellite AKARI . The sample is selected from the 9-­month Swift /BAT survey in the 14–­195 keV band and all of them have measured X-­ray spectra at E \lesssim 10 keV . These X-­ray spectra provide measurements of the neutral hydrogen column density ( N _ { H } ) towards the AGNs . We use the 3.3 \micron PAH luminosity ( L _ { 3.3 { \micron } } ) as a proxy for star formation activity and hard X-ray luminosity ( L _ { 14 - 195 keV } ) as an indicator of the AGN activity . We search for possible difference of star-­formation activity between type 1 ( un-absorbed ) and type 2 ( absorbed ) AGNs . We have made several statistical analyses taking the upper-limits of the PAH lines into account utilizing survival analysis methods . The results of our \log ( L _ { 14 - 195 keV } ) versus \log ( L _ { 3.3 { \micron } } ) regression shows a positive correlation and the slope for the type 1/unobscured AGNs is steeper than that of type 2/obscured AGNs at a 3 \sigma level . Also our analysis show that the circum-nuclear star-formation is more enhanced in type 2/absorbed AGNs than type 1/un-absorbed AGNs for low X-ray luminosity/low Eddington ratio AGNs , while there is no significant dependence of star-formation activities on the AGN type in the high X-ray luminosities/Eddington ratios .