  We explore the relationships between the 3.3 {\mu}m 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 ($N_{\rm H}$) towards the AGNs. We use the 3.3 {\mu}m
PAH luminosity ($L_{\rm 3.3{\mu}m}$) as a proxy for star formation activity and
hard X-ray luminosity ($L_{\rm 14-195keV}$) 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 $\log(L_{\rm
14-195keV})$ versus $\log(L_{\rm 3.3{\mu}m})$ 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.
