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 $>2rm ~keV$) 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.
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