Using the InfraRed Camera (IRC) on board the infrared astronomical satellite AKARI we study the 3.3 μm polycyclic aromatic hydrocarbon (PAH) feature and its connection to active galactic nucleus (AGN) properties for a sample of 54 hard X-ray selected bright AGN, including both Seyfert 1 and Seyfert 2 type objects. The sample is selected from the 9-month Swift/BAT survey in the 14-195 keV band and all of the sources have known neutral hydrogen column densities (NH). The 3.3 μm PAH luminosity (L3:3μm) is used as a proxy for star-formation (SF) activity and hard X-ray luminosity (L14-195keV) as an indicator of the AGN power. We explore for possible dierence of SF activity between type 1 (un-absorbed) and type 2 (absorbed) AGN. We use several statistical analyses taking the upper-limits of the PAH lines into account utilizing survival analysis methods. The results of our log(L14-195keV) versus log(L3:3μm) regression shows a positive correlation and the slope for the type 1/unobscured AGN is steeper than that of type 2/obscured AGN at a 3σ level. Also our analysis shows that the circum-nuclear SF is more enhanced in type 2/absorbed AGN than type 1/un-absorbed AGN for low L14-195keV luminosity/low Eddington ratio AGN, while there is no significant dependence of SF activity on the AGN type in the high L14-195keV luminosities/Eddington ratios.