  We present a systematic X-ray and multiwavelength study of a sample of 47
active galactic nuclei (AGNs) with reverberation-mapping measurements. This
sample includes 21 super-Eddington accreting AGNs and 26 sub-Eddington
accreting AGNs. Using high-state observations with simultaneous X-ray and
UV/optical measurements, we investigate whether super-Eddington accreting AGNs
exhibit different accretion disk-corona connections compared to sub-Eddington
accreting AGNs. We find tight correlations between the X-ray-to-UV/optical
spectral slope parameter ($\alpha_{\rm OX}$) and the monochromatic luminosity
at $2500~\r{A}$ ($L_{\rm 2500~\r{A}}$) for both the super- and sub-Eddington
subsamples. The best-fit $\alpha_{\rm OX}-L_{\rm 2500~\r{A}}$ relations are
consistent overall, indicating that super-Eddington accreting AGNs are not
particularly X-ray weak in general compared to sub-Eddington accreting AGNs. We
find dependences of $\alpha_{\rm OX}$ on both the Eddington ratio ($L_{\rm
Bol}/L_{\rm Edd}$) and black hole mass ($M_{\rm BH}$) parameters for our full
sample. A multi-variate linear regression analysis yields $\alpha_{\rm
OX}=-0.13 {\rm log}(L_{\rm Bol}/L_{\rm Edd})-0.10 {\rm log}M_{\rm BH}-0.69$,
with a scatter similar to that of the $\alpha_{\rm OX}-L_{\rm 2500~\r{A}}$
relation. The hard (rest-frame $>2\rm ~keV$) X-ray photon index ($\Gamma$) is
strongly correlated with $L_{\rm Bol}/L_{\rm Edd}$ for the full sample and the
super-Eddington subsample, but these two parameters are not significantly
correlated for the sub-Eddington subsample. A fraction of super-Eddington
accreting AGNs show strong X-ray variability, probably due to small-scale gas
absorption, and we highlight the importance of employing high-state (intrinsic)
X-ray radiation to study the accretion disk-corona connections in AGNs.
