Because the disc--jet coupling likely depends on various properties of sources probed, the sample control is always an important but challenging task. In this work, we re-analyzed the INTEGRAL hard X-ray-selected sample of Seyfert galaxies. We only consider sources that have measurements in black hole mass, and luminosities in radio and X-rays. Our sample includes 64 sources, consists of both bright AGNs and low-luminosity ones. We first find that, because of the similarity in the $L_{HX}/L_X$ distribution, the X-ray origin of radio-loud Seyferts may be the same to that of radio-quiet ones, where we attribute to the hot accretion flow (or similarly, the corona). We then investigate the connections between luminosities in radio and X-rays. Since our sample suffers a selection bias of a black hole mass $M_{BH}$ dependence on $L_X/L_{Edd}$, we focus on the correlation slope $xi_X$ between the radio (at 1.4 GHz) and X-ray luminosities in Eddington unit, i.e. $(L_R/L_{Edd})propto(L_X/L_{Edd})^{xi_X}$. We classify the sources according to various properties, i.e. 1) Seyfert classification, 2) radio loudness, and 3) radio morphology. We find that, despite these differences in classification, all the sources in our sample are consistent with a universal correlation slope $xi_X$, with $xi_X=0.77pm0.10$. This is unexpected, considering various possible radio emitters in radio-quiet systems. For the jet interpretation, our result may suggest a common/universal but to be identified jet launching mechanism among all the Seyfert galaxies, while properties like black hole spin and magnetic field strength only play secondary roles. We further estimate the jet production efficiency $eta_{jet}$ of Seyfert galaxies, which is $eta_{jet}approx1.9^{+0.9}_{-1.5}times10^{-4}$ on average. We also find that $eta_{jet}$ increases as the system goes fainter.
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